Tootfinder

Symmetries of the cyclic nerve
David Ayala, Aaron Mazel-Gee, Nick Rozenblyum
https://arxiv.org/abs/2405.03897 https://arxiv.org/pdf/2…

Symmetries of the cyclic nerve
We undertake a systematic study of the Hochschild homology, i.e. (the geometric realization of) the cyclic nerve, of $(\infty,1)$-categories (and more generally of category-objects in an $\infty$-category), as a version of factorization homology. In order to do this, we codify $(\infty,1)$-categories in terms of quiver representations in them. By examining a universal instance of such Hochschild homology, we explicitly identify its natural symmetries, and construct a non-stable version of the c…

On one-orbit cyclic subspace codes of $\mathcal{G}_q(n,3)$
Chiara Castello, Olga Polverino, Ferdinando Zullo
https://arxiv.org/abs/2405.01652 https://

On one-orbit cyclic subspace codes of $\mathcal{G}_q(n,3)$
Subspace codes have recently been used for error correction in random network coding. In this work, we focus on one-orbit cyclic subspace codes. If $S$ is an $\mathbb{F}_q$-subspace of $\mathbb{F}_{q^n}$, then the one-orbit cyclic subspace code defined by $S$ is \[ \mathrm{Orb}(S)=\{αS \colon α\in \mathbb{F}_{q^n}^*\}, \]where $αS=\lbrace αs \colon s\in S\rbrace$ for any $α\in \mathbb{F}_{q^n}^*$. Few classification results of subspace codes are known, therefore it is quite natural to init…

Nonassociative cyclic algebras and the semiassociative Brauer monoid
S Pumpluen
https://arxiv.org/abs/2403.03263 https://arxiv.org/pd…

Nonassociative cyclic algebras and the semiassociative Brauer monoid
We look at classes of semiassociative algebras, with an emphasis on those that canonically generalize associative (generalized) cyclic algebras, and at their behaviour in the semiassociative Brauer monoid defined by Blachar, Haile, Matri, Rein, and Vishne. A possible way to generalize this monoid in characteristic $p$ that includes nonassociative differential algebras is briefly considered.

Data-Based In-Cylinder Pressure Model with Cyclic Variations for Combustion Control: A RCCI Engine Application
Maarten Vlaswinkel, Frank Willems
https://arxiv.org/abs/2403.03602 <…

Data-Based In-Cylinder Pressure Model with Cyclic Variations for Combustion Control: A RCCI Engine Application
Cylinder pressure-based control is a key enabler for advanced pre-mixed combustion concepts. Besides guaranteeing robust and safe operation, it allows for cylinder pressure and heat release shaping. This requires fast control-oriented combustion models. Over the years, mean-value models have been proposed that can predict combustion measures (e.g., Gross Indicated Mean Effective Pressure, or the crank angle where 50% of the total heat is released) or models that predict the full in-cylinder pre…

Non-cyclicity and polynomials in Dirichlet-type spaces of the unit ball
Dimitrios Vavitsas, Konstantinos Zarvalis
https://arxiv.org/abs/2405.03020 https://…

Non-cyclicity and polynomials in Dirichlet-type spaces of the unit ball
We give a description of the intersection of the zero set with the unit sphere of a zero-free polynomial in the unit ball of $\mathbb{C}^n$. This description leads to the formulation of a conjecture regarding the characterization of polynomials that are cyclic in Dirichlet-type spaces in the unit ball of $\mathbb{C}^n$. Furthermore, we answer partially ascertaining whether an arbitrary polynomial is not cyclic.

Zeroes of Rankin-Selberg $L$-functions and the trace formula
Tian An Wong
https://arxiv.org/abs/2405.02998 https://arxiv.org/pdf/2405…

Zeroes of Rankin-Selberg $L$-functions and the trace formula
We express the contribution of certain maximal parabolic Eisenstein series to the spectral side of the Arthur--Selberg trace formula for GL$(n)$ in terms of zeroes of Rankin--Selberg $L$-functions, generalizing previous results for GL(2) and Hecke $L$-functions. As applications, we prove a lower bound for the sum of these zeroes, and a base change relation between the zeroes in the case $n=2$ for cyclic extensions of prime degree.

This https://arxiv.org/abs/2309.15041 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Estimation of fatigue life of TiN coatings using cyclic micro-impact testing
This paper studies the behaviour of a thin titanium nitride (TiN) coating (1.5 um thick) on a tool steel substrate material under dynamic and cyclic impacts through an approach combining experimental testing and computational modelling. Dynamic impact testing was used to investigate the load-dependent dynamic hardness and assess the energy-dissipation capabilities of the coating system. In cyclic impact tests, the materials experienced permanent plastic deformation in each cycle, ultimately lea…

This https://arxiv.org/abs/2304.00762 has been replaced.
link: https://scholar.google.com/scholar?q=a

The (r, δ)-Locality of Repeated-Root Cyclic Codes with Prime Power Lengths
Locally repairable codes (LRCs) are designed for distributed storage systems to reduce the repair bandwidth and disk I/O complexity during the storage node repair process. A code with $(r,δ)$-locality (also called an $(r,δ)$-LRC) can simultaneously repair up to $δ-1$ symbols in a codeword by accessing at most $r$ other symbols in the codeword. In this paper, we propose a new method to calculate the $(r,δ)$-locality of cyclic codes. Initially, we give a description of the algebraic structure…

Cyclic Higgs bundles and the Toledo invariant
Oscar Garc\'ia-Prada, Miguel Gonz\'alez
https://arxiv.org/abs/2403.00415 https://

Cyclic Higgs bundles and the Toledo invariant
Let $G$ be a complex semisimple Lie group and $\mathfrak g$ its Lie algebra. In this paper, we study a special class of cyclic Higgs bundles constructed from a $\mathbb Z$-grading $\mathfrak g = \bigoplus_{j=1-m}^{m-1}\mathfrak g_j$ by using the natural representation $G_0 \to GL(\mathfrak g_1 \oplus \mathfrak g_{1-m})$, where $G_0 \le G$ is the connected subgroup corresponding to $\mathfrak g_0$. The resulting Higgs pairs include $G^{\mathbb R}$-Higgs bundles for $G^{\mathbb R} \le G$ a real f…

This https://arxiv.org/abs/2304.06276 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Distinguishing 2-knots admitting circle actions by fundamental groups
A 2-sphere embedded in the 4-sphere invariant under a circle action is called a branched twist spin. A branched twist spin is constructed from a 1-knot in the 3-sphere and a pair of coprime integers uniquely. In this paper, we study, for each pair of coprime integers, if two different 1-knots yield the same branched twist spin, and prove that such a pair of 1-knots does not exist in most cases. Fundamental groups of 3-orbifolds of cyclic type are obtained as quotient groups of the fundamental g…

A group action on cyclic compositions and $\gamma$-positivity
Shishuo Fu, Jie Yang
https://arxiv.org/abs/2403.00378 https://arxiv.org…

A group action on cyclic compositions and $γ$-positivity
Let $w_{n,k,m}$ be the number of Dyck paths of semilength $n$ with $k$ occurrences of $UD$ and $m$ occurrences of $UUD$. We establish in two ways a new interpretation of the numbers $w_{n,k,m}$ in terms of plane trees and internal nodes. The first way builds on a new characterization of plane trees that involves cyclic compositions. The second proof utilizes a known interpretation of $w_{n,k,m}$ in terms of plane trees and leaves, and a recent involution on plane trees constructed by Li, Lin, a…

This https://arxiv.org/abs/2402.04592 has been replaced.
link: https://scholar.google.com/scholar?q=a

Frattini subgroups of hyperbolic-like groups
We study Frattini subgroups of various generalizations of hyperbolic groups. For any countable group $G$ admitting a general type action on a hyperbolic space $S$, we show that the induced action of the Frattini subgroup $Φ(G)$ on $S$ has bounded orbits. This implies that $Φ(G)$ is "small" compared to $G$; in particular, $|G:Φ(G)|=\infty$. In contrast, for any finitely generated non-cyclic group $Q$ with $Φ(Q)=\{ 1\}$, we construct an infinite lacunary hyperbolic group $L$ such th…

Ambush strategy enhances organisms' performance in rock-paper-scissors games
R. Barbalho, S. Rodrigues, M. Tenorio, J. Menezes
https://arxiv.org/abs/2405.02674

Ambush strategy enhances organisms' performance in rock-paper-scissors games
We study a five-species cyclic system wherein individuals of one species strategically adapt their movements to enhance their performance in the spatial rock-paper-scissors game. Environmental cues enable the awareness of the presence of organisms targeted for elimination in the cyclic game. If the local density of target organisms is sufficiently high, individuals move towards concentrated areas for direct attack; otherwise, they employ an ambush tactic, maximising the chances of success by ta…

This https://arxiv.org/abs/2403.14571 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Trivial source character tables of Frobenius groups of type $(C_p \times C_p) \rtimes H$
Let $p$ be a prime number. We compute the trivial source character tables of finite Frobenius groups $G$ with an abelian Frobenius complement $H$ and an elementary abelian Frobenius kernel of order $p^2$. More precisely, we deal with all infinite families of such groups which occur in the two extremal cases for the fusion of $p$-subgroups: the case in which there exists exactly one $G$-conjugacy class of non-trivial cyclic $p$-subgroups, and the case in which there exist exactly $p+1$ distinct …

KIAS Lectures on Symplectic Aspects of Degenerations
Jonathan David Evans
https://arxiv.org/abs/2403.03519 https://arxiv.org/pdf/2403…

KIAS Lectures on Symplectic Aspects of Degenerations
This is a series of three lectures I gave at the Korea Institute of Advanced Study in June 2019 at a workshop about "Algebraic and Symplectic Aspects of Degenerations of Complex Surfaces". I focus on the symplectic aspects, in particular on the case of cyclic quotient surface singularities. These notes have been available on a public Git repository since 2019, and I noticed that people occasionally cited them in the years since. For that reason, I decided to post them on arXiv for a more perman…

A topological characterization of the existence of w-stable sets
Athanasios Andrikopoulos, Nikolaos Sampanis
https://arxiv.org/abs/2403.04512 https://

A topological characterization of the existence of w-stable sets
The theory of optimal choice sets is a solution theory that has a long and well-established tradition in social choice and game theories. Some of important general solution concepts of choice problems when the set of best alternatives does not exist (this problem occurs when the preferences yielded by an economic process are cyclic) is the Stable Set (Von Neumann-Morgenstern set) and its variants (Generalized Stable set, Extended Stable set, m-Stable set and w-Stable set). The theory of w-stabl…

Data based constitutive modelling of rate independent inelastic effects in composite cables using Preisach hysteresis operators
Davide Manfredo, Vanessa D\"orlich, Joachim Linn, Martin Arnold
https://arxiv.org/abs/2403.03531

Data based constitutive modelling of rate independent inelastic effects in composite cables using Preisach hysteresis operators
This contribution aims at introducing first steps to develop hysteresis operator type inelastic constitutive laws for Cosserat rods for the simulation of cables composed of complex interior components. Motivated by the basic elements of Cosserat rod theory, we develop a specific approach to constitutive modelling adapted for this application. Afterwards, we describe the hysteretical behaviour arising from cyclic bending experiments on cables by means of the Preisach operator. As shown in pure b…

This https://arxiv.org/abs/2305.06719 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Geodesically complete cyclic cosmologies and entropy
We demonstrate that there exists a class of cyclic cosmological models, such that these models can in principle solve the problem of the entropy growth, and are at the same time geodesically complete. We thus show that some recently stated conclusions, according to which cyclic cosmologies solving the problem of entropy growth can not be geodesically complete due to the Borde-Guth-Vilenkin (BGV) theorem, are not justified. We also add a short conceptual discussion on entropy and cyclic cosmolog…

Zeroes of Rankin-Selberg $L$-functions and the trace formula
Tian An Wong
https://arxiv.org/abs/2405.02998 https://arxiv.org/pdf/2405…

Zeroes of Rankin-Selberg $L$-functions and the trace formula
We express the contribution of certain maximal parabolic Eisenstein series to the spectral side of the Arthur--Selberg trace formula for GL$(n)$ in terms of zeroes of Rankin--Selberg $L$-functions, generalizing previous results for GL(2) and Hecke $L$-functions. As applications, we prove a lower bound for the sum of these zeroes, and a base change relation between the zeroes in the case $n=2$ for cyclic extensions of prime degree.

Non-wellfounded parsimonious proofs and non-uniform complexity
Matteo Acclavio, Gianluca Curzi, Giulio Guerrieri
https://arxiv.org/abs/2404.03311 https://<…

Non-wellfounded parsimonious proofs and non-uniform complexity
In this paper we investigate the complexity-theoretical aspects of cyclic and non-wellfounded proofs in the context of parsimonious logic, a variant of linear logic where the exponential modality ! is interpreted as a constructor for streams over finite data. We present non-wellfounded parsimonious proof systems capturing the classes $\mathbf{FPTIME}$ and $\mathbf{FP}/\mathsf{poly}$. Soundness is established via a polynomial modulus of continuity for continuous cut-elimination. Completeness rel…

This https://arxiv.org/abs/2403.03602 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Data-Based In-Cylinder Pressure Model with Cyclic Variations for Combustion Control: A RCCI Engine Application
Cylinder pressure-based control is a key enabler for advanced pre-mixed combustion concepts. Besides guaranteeing robust and safe operation, it allows for cylinder pressure and heat release shaping. This requires fast control-oriented combustion models. Over the years, mean-value models have been proposed that can predict combustion measures (e.g., Gross Indicated Mean Effective Pressure, or the crank angle where 50% of the total heat is released) or models that predict the full in-cylinder pre…

Comparing Personalized Relevance Algorithms for Directed Graphs
Luca Cavalcanti, Cristian Consonni, Martin Brugnara, David Laniado, Alberto Montresor
https://arxiv.org/abs/2405.02261

Comparing Personalized Relevance Algorithms for Directed Graphs
We present an interactive Web platform that, given a directed graph, allows identifying the most relevant nodes related to a given query node. Besides well-established algorithms such as PageRank and Personalized PageRank, the demo includes Cyclerank, a novel algorithm that addresses some of their limitations by leveraging cyclic paths to compute personalized relevance scores. Our demo design enables two use cases: (a) algorithm comparison, comparing the results obtained with different algorith…

A group action on cyclic compositions and $\gamma$-positivity
Shishuo Fu, Jie Yang
https://arxiv.org/abs/2403.00378 https://arxiv.org…

A group action on cyclic compositions and $γ$-positivity
Let $w_{n,k,m}$ be the number of Dyck paths of semilength $n$ with $k$ occurrences of $UD$ and $m$ occurrences of $UUD$. We establish in two ways a new interpretation of the numbers $w_{n,k,m}$ in terms of plane trees and internal nodes. The first way builds on a new characterization of plane trees that involves cyclic compositions. The second proof utilizes a known interpretation of $w_{n,k,m}$ in terms of plane trees and leaves, and a recent involution on plane trees constructed by Li, Lin, a…

This https://arxiv.org/abs/2208.09420 has been replaced.
link: https://scholar.google.com/scholar?q=a

The evaluation of the rate constants for a reversible unimolecular hydrogen transfer reaction that involves a cyclic transition state
Intermolecular hydrogen transfer free radical reactions are common in the combustion process and in a number of organic chemistry reactions. Therefore, evaluating the pressure and temperature-dependent rate constants of them is of great importance. Basing on microcanonical Rice-Ramsperger-Kassel-Marcus (RRKM) theory, tunnelling correction, and internal rotation correction, we present a simple model that is able to give an estimate of the desired rate constants of a reversible unimolecular react…

Cyclicity of the shift operator and a related completeness problem in de Branges-Rovnyak spaces
Emmanuel FricainLPP, Romain LebretonLPP
https://arxiv.org/abs/2403.04335

Cyclicity of the shift operator and a related completeness problem in de Branges-Rovnyak spaces
In this paper, we study the cyclic vectors of the shift operator $S_b$ acting on de Branges-Rovnyak space $\mathcal H(b)$ associated to a non-extreme point of the closed unit ball of $H^\infty$. We highlight an interesting link with a completeness problem that we study using the Cauchy transform. This enables us to obtain some nice consequences on cyclicity.

This https://arxiv.org/abs/2306.08425 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Fine structures inside the PreLie operad revisited
We prove a conjecture of Chapoton from 2010 stating that the pre-Lie operad, as a Lie algebra in the symmetric monoidal category of linear species, is freely generated by the free operad on the species of cyclic Lie elements.

Equivariant cohomology for cyclic groups
Samik Basu, Pinka Dey
https://arxiv.org/abs/2403.00362 https://arxiv.org/pdf/2403.00362

Equivariant cohomology for cyclic groups
In this paper, we compute the $RO(C_n)$-graded coefficient ring of equivariant cohomology for cyclic groups $C_n$, in the case of Burnside ring coefficients, and in the case of constant coefficients. We use the invertible Mackey functors under the box product to reduce the gradings in the computation from $RO(C_n)$ to those expressable as combinations of $λ^d$ for divisors $d$ of $n$, where $λ$ is the inclusion of $C_n$ in $S^1$ as the roots of unity. We make explicit computations for the geo…

Cyclic measurements and simplified quantum state tomography
Victor Gonzalez Avella, Jakub Czartowski, Dardo Goyeneche, Karol \.Zyczkowski
https://arxiv.org/abs/2404.18847

Cyclic measurements and simplified quantum state tomography
Tomographic reconstruction of quantum states plays a fundamental role in benchmarking quantum systems and retrieving information from quantum computers. Among the informationally complete sets of quantum measurements the tight ones provide a linear reconstruction formula and minimize the propagation of statistical errors. However, implementing tight measurements in the lab is challenging due to the high number of required measurement projections, involving a series of experimental setup prepara…

Prof. Grubbs was inspired to prepare an introductory lecture on PQC for today’s EECS 388 lecture.

"Against the Void": An Interview and Survey Study on How Rust Developers Use Unsafe Code
Ian McCormack, Tomas Dougan, Sam Estep, Hanan Hibshi, Jonathan Aldrich, Joshua Sunshine
https://arxiv.org/abs/2404.02230

"Against the Void": An Interview and Survey Study on How Rust Developers Use Unsafe Code
The Rust programming language is an increasingly popular choice for systems programming, since it can statically guarantee memory safety without automatic garbage collection. Rust provides its safety guarantees by restricting aliasing and mutability, but many key design patterns, such as cyclic aliasing and multi-language interoperation, must bypass these restrictions. Rust's $\texttt{unsafe}$ keyword enables features that developers can use to implement these patterns, and the Rust ecosystem i…

Deviations for generalized tiling billiards in cyclic polygons
Magali Jay
https://arxiv.org/abs/2402.15765 https://arxiv.org/pdf/2402…

Deviations for generalized tiling billiards in cyclic polygons
This work continues the study of tiling billiards, a class of dynamical system introduced by Davis et al. in 2018. We develop the study of generalized tiling billiards in a cyclic polygon. This work shows that the behavior of generalized tiling billiards in cyclic N-gons with N > 4 is considerably different from that of triangular and quadrilateral tiling billiards studied before. Indeed, we exhibit an open set of generalized tiling billiard trajectories deviating sublinearly from their asympto…

The Hurwitz tree obstruction for the refined local lifting problem
Huy Dang
https://arxiv.org/abs/2405.01845 https://arxiv.org/pdf/24…

The Hurwitz tree obstruction for the refined local lifting problem
In this manuscript, we formulate the differential Hurwitz tree obstructions for the refined local lifting problem. We specifically explore the circumstances under which these obstructions vanish for cyclic covers. The constructions presented in this paper will be used to address the refined local lifting problem in our forthcoming works.

Construction of quantum codes from $(\gamma,\Delta)$-cyclic codes
Om Prakash, Shikha Patel, Habibul Islam
https://arxiv.org/abs/2404.01904 https://<…

Construction of quantum codes from $(γ,Δ)$-cyclic codes
Let $\mathbb{F}_q$ be the finite field of $q=p^m$ elements where $p$ is a prime and $m$ is a positive integer. This paper considers $(γ,Δ)$-cyclic codes over a class of finite commutative non-chain rings $\mathscr{R}_{q,s}=\mathbb{F}_q[v_1,v_2,\dots,v_s]/\langle v_i-v_i^2,v_iv_j=v_jv_i=0\rangle$ where $γ$ is an automorphism of $\mathscr{R}_{q,s}$, $Δ$ is a $γ$-derivation of $\mathscr{R}_{q,s}$ and $1\leq i\neq j\leq s$ for a positive integer $s$. Here, we show that a $(γ,Δ)$-cyclic code …

This https://arxiv.org/abs/2106.09984 has been replaced.
link: https://scholar.google.com/scholar?q=a

Some factorization properties of idealization in commutative rings with zero divisors
We study some factorization properties of the idealization $R \mathop{(\! + \! )} M$ of a module $M$ in a commutative ring $R$ which is not necessarily a domain. We show that $R \mathop{(\! + \! )} M$ is ACCP if and only if $R$ is ACCP and $M$ satisfies ACC on its cyclic submodules. We give an example to show that the BF property is not necessarily preserved in idealization, and give some conditions under which $R \mathop{(\! + \! )} M$ is a BFR. We also characterize the idealization rings whic…

This https://arxiv.org/abs/2402.04468 has been replaced.
link: https://scholar.google.com/scholar?q=a

Combinatorial 2d higher topological quantum field theory from a local cyclic $A_\infty$ algebra
We construct combinatorial analogs of 2d higher topological quantum field theories. We consider triangulations as vertices of a certain CW complex $Ξ$. In the "flip theory," cells of $Ξ_\mathrm{flip}$ correspond to polygonal decompositions obtained by erasing the edges in a triangulation. These theories assign to a cobordism $Σ$ a cochain $Z$ on $Ξ_\mathrm{flip}$ constructed as a contraction of structure tensors of a cyclic $A_\infty$ algebra $V$ assigned to polygons. The cyclic $A_\infty$ …

The Magic Number Conjecture for the $m=2$ amplituhedron and Parke-Taylor identities
Matteo Parisi, Melissa Sherman-Bennett, Ran Tessler, Lauren Williams
https://arxiv.org/abs/2404.03026

The Magic Number Conjecture for the $m=2$ amplituhedron and Parke-Taylor identities
The amplituhedron $\mathcal{A}_{n,k,m}$ is a geometric object introduced in the context of scattering amplitudes in $\mathcal{N}=4$ super Yang Mills. It generalizes the positive Grassmannian (when $n=k+m$), cyclic polytopes (when $k=1$), and the bounded complex of the cyclic hyperplane arrangement (when $m=1$). Of substantial interest are the tilings of the amplituhedron, which are analogous to triangulations of a polytope. Karp, Williams and Zhang (2020) observed that the known tilings of $\ma…

Learning Cyclic Causal Models from Incomplete Data
Muralikrishnna G. Sethuraman, Faramarz Fekri
https://arxiv.org/abs/2402.15625 https://

Learning Cyclic Causal Models from Incomplete Data
Causal learning is a fundamental problem in statistics and science, offering insights into predicting the effects of unseen treatments on a system. Despite recent advances in this topic, most existing causal discovery algorithms operate under two key assumptions: (i) the underlying graph is acyclic, and (ii) the available data is complete. These assumptions can be problematic as many real-world systems contain feedback loops (e.g., biological systems), and practical scenarios frequently involve…

Cyclic Group Spectra for Some Small Relation Algebras
Jeremy F. Alm, Ashlee Bostic, Claire Chenault, Kenyon Coleman, Chesney Culver
https://arxiv.org/abs/2403.15939

Cyclic Group Spectra for Some Small Relation Algebras
The question of characterizing the (finite) representable relation algebras in a ``nice" way is open. The class $\mathbf{RRA}$ is known to be not finitely axiomatizable in first-order logic. Nevertheless, it is conjectured that ``almost all'' finite relation algebras are representable. All finite relation algebras with three or fewer atoms are representable. So one may ask, Over what cardinalities of sets are they representable? This question was answered completely by Andréka and Maddux (``…

{spiralize} can be used to highlight cyclic data, e.g. multi year time series. #rstats

This https://arxiv.org/abs/2110.11655 has been replaced.
link: https://scholar.google.com/scholar?q=a

Parafree graphs of groups with cyclic edge groups
We establish a combination theorem for parafree groups. These groups were introduced by Baumslag in the sixties. One of the current motivations for a better understanding of their structure is that they show up naturally in connection with Remeslennikov's conjecture on the profinite rigidity of free groups. In this article, we determine when the fundamental group of a finite graph of groups with cyclic edge groups is parafree.

This https://arxiv.org/abs/2402.00951 has been replaced.
link: https://scholar.google.com/scholar?q=a

Comparing growth of titania and carbonaceous dusty nanoparticles in weakly magnetised capacitively coupled plasmas
This study investigates the growth cycles of titania and carbonaceous dusty nanoparticles in capacitively coupled radiofrequency plasmas, focusing on the impact of weak magnetic field of approximately 480 Gauss. The growth of dusty nanoparticles in these plasmas is cyclic, with particles reaching their maximum size and subsequently moving out of the plasma, followed by the initiation of a new particle growth cycle. We compare the growth of titania and carbonaceous dusty particles in the presenc…

A Cyclic Spectroscopy Scintillation Study of PSR B1937 21 I. Demonstration of Improved Scintillometry
Jacob E. Turner, Timothy Dolch, James M. Cordes, Stella K. Ocker, Daniel R. Stinebring, Shami Chatterjee, Maura A. McLaughlin, Victoria E. Catlett, Cody Jessup, Nathaniel Jones, Christopher Scheithauer
https://arxiv.org/abs/2404…

A Cyclic Spectroscopy Scintillation Study of PSR B1937+21 I. Demonstration of Improved Scintillometry
We use cyclic spectroscopy to perform high frequency-resolution analyses of multi-hour baseband Arecibo observations of the millisecond pulsar PSR B1937+21. This technique allows for the examination of scintillation features in far greater detail than is otherwise possible under most pulsar timing array observing setups. We measure scintillation bandwidths and timescales in each of eight subbands across a 200 MHz observing band in each observation. Through these measurements we obtain robust, i…

Non-Abelian extensions of degree $p^3$ and $p^4$ in characteristic $p>2$
Grant Moles
https://arxiv.org/abs/2403.02442 https://arxi…

Non-Abelian extensions of degree $p^3$ and $p^4$ in characteristic $p>2$
This paper describes in terms of Artin-Schreier equations field extensions whose Galois group is isomorphic to any of the four non-cyclic groups of order $p^3$ or the ten non-Abelian groups of order $p^4$, $p$ an odd prime, over a field of characteristic $p$.

Cyclic branched covers of Seifert links and properties related to the $ADE$ link conjecture
Steven Boyer, Cameron McA. Gordon, Ying Hu
https://arxiv.org/abs/2402.15914

Cyclic branched covers of Seifert links and properties related to the $ADE$ link conjecture
In this article we show that all cyclic branched covers of a Seifert link have left-orderable fundamental groups, and therefore admit co-oriented taut foliations and are not $L$-spaces, if and only if it is not an $ADE$ link up to orientation. This leads to a proof of the $ADE$ link conjecture for Seifert links. When $L$ is an $ADE$ link up to orientation, we determine which of its canonical $n$-fold cyclic branched covers $Σ_n(L)$ have non-left-orderable fundamental groups. In addition, we gi…

This https://arxiv.org/abs/2212.08345 has been replaced.
link: https://scholar.google.com/scholar?q=a

Open Gromov-Witten invariants from the Fukaya category
This paper proposes a framework to show that the Fukaya category of a symplectic manifold $X$ determines the open Gromov-Witten invariants of Lagrangians $L \subset X$. We associate to an object in an $A_\infty$-category an extension of the negative cyclic homology, called \emph{relative cyclic homology}. We extend the Getzler-Gauss-Manin connection to relative cyclic homology. Then, we construct (under simplifying technical assumptions) a relative cyclic open-closed map, which maps the relativ…

Completely fixed point free isometry and cyclic orbifold of lattice vertex operator algebras
Hsian-Yang Chen, Ching Hung Lam
https://arxiv.org/abs/2402.13621

Completely fixed point free isometry and cyclic orbifold of lattice vertex operator algebras
We continue our study of cyclic orbifolds of lattice vertex operator algebras and their full automorphism groups. We consider some special isometry $g\in O(L)$ such that $g^i$ is fixed point free on $L$ for any $1\leq i\leq |g|-1$. We show that when $L_2=\emptyset$ and $g^i$ is fixed point free on $L$ for any $1\leq i\leq |g|-1$, $V_L^{\hat{g}}$ has extra automorphisms implies either (1) the order of $g$ is a prime or (2) $L$ is isometric to the Leech lattice or some coinvar…

Generalized cyclic symmetric decompositions for the matrix multiplication tensor
Charlotte Vermeylen, Marc Van Barel
https://arxiv.org/abs/2404.16699 https…

Generalized cyclic symmetric decompositions for the matrix multiplication tensor
In this paper we propose a new generalized cyclic symmetric structure in the factor matrices of polyadic decompositions of matrix multiplication tensors for non-square matrix multiplication to reduce the number of variables in the optimization problem and in this way improve the convergence.

Cyclic Lie-Rinehart algebras
Daniel Beltita, Alina Dobrogowska, Grzegorz Jakimowicz
https://arxiv.org/abs/2402.10845 https://arxiv.or…

Cyclic Lie-Rinehart algebras
We study Lie-Rinehart algebra structures in the framework provided by a duality pairing of modules over a unital commutative associative algebra. Thus, we construct examples of Lie brackets corresponding to a fixed anchor map whose image is a cyclic submodule of the derivation module, and therefore we call them cyclic Lie-Rinehart algebras. In a very special case of our construction, these brackets turn out to be related to certain differential operators that occur in mathematical physics.

Reed-Solomon Codes over Cyclic Polynomial Ring with Lower Encoding/Decoding Complexity
Wenhao Liu, Zhengyi Jiang, Zhongyi Huang, Linqi Song, Hanxu Hou
https://arxiv.org/abs/2405.01043

Reed-Solomon Codes over Cyclic Polynomial Ring with Lower Encoding/Decoding Complexity
Reed-Solomon (RS) codes are constructed over a finite field that have been widely employed in storage and communication systems. Many fast encoding/decoding algorithms such as fast Fourier transform (FFT) and modular approach are designed for RS codes to reduce the encoding/decoding complexity defined as the number of XORs involved in the encoding/decoding procedure. In this paper, we present the construction of RS codes over the cyclic polynomial ring $ \mathbb{F}_2[x]/(1+x+\ldots+x^{p-1})$ an…

Deep Learning-based Modulation Classification of Practical OFDM Signals for Spectrum Sensing
Byungjun Kim, Christoph Mecklenbr\"auker, Peter Gerstoft
https://arxiv.org/abs/2403.19292

Deep Learning-based Modulation Classification of Practical OFDM Signals for Spectrum Sensing
In this study, the modulation of symbols on OFDM subcarriers is classified for transmissions following Wi-Fi~6 and 5G downlink specifications. First, our approach estimates the OFDM symbol duration and cyclic prefix length based on the cyclic autocorrelation function. We propose a feature extraction algorithm characterizing the modulation of OFDM signals, which includes removing the effects of a synchronization error. The obtained feature is converted into a 2D histogram of phase and amplitude …

CycPUF: Cyclic Physical Unclonable Function
Michael Dominguez, Amin Rezaei
https://arxiv.org/abs/2402.08084 https://arxiv.org/pdf/240…

CycPUF: Cyclic Physical Unclonable Function
Physical Unclonable Functions (PUFs) leverage manufacturing process imperfections that cause propagation delay discrepancies for the signals traveling along these paths. While PUFs can be used for device authentication and chip-specific key generation, strong PUFs have been shown to be vulnerable to machine learning modeling attacks. Although there is an impression that combinational circuits must be designed without any loops, cyclic combinational circuits have been shown to increase design se…

This https://arxiv.org/abs/2309.16762 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A short proof of Tomita's theorem
Tomita-Takesaki theory associates a positive operator called the "modular operator" with a von Neumann algebra and a cyclic-separating vector. Tomita's theorem says that the unitary flow generated by the modular operator leaves the algebra invariant. I give a new, short proof of this theorem which only uses the analytic structure of unitary flows, and which avoids operator-valued Fourier transforms (as in van Daele's proof) and operator-valued Mellin transforms (as in Zsidó's and Woronowicz's …

This https://arxiv.org/abs/2106.11798 has been replaced.
link: https://scholar.google.com/scholar?q=a

The failure of cut-elimination in cyclic proof for first-order logic with inductive definitions
A cyclic proof system is a proof system whose proof figure is a tree with cycles. The cut-elimination in a proof system is fundamental. It is conjectured that the cut-elimination in the cyclic proof system for first-order logic with inductive definitions does not hold. This paper shows that the conjecture is correct by giving a sequent not provable without the cut rule but provable in the cyclic proof system.

This https://arxiv.org/abs/2110.11655 has been replaced.
link: https://scholar.google.com/scholar?q=a

Parafree graphs of groups with cyclic edge groups
We establish a combination theorem for parafree groups. These groups were introduced by Baumslag in the sixties. One of the current motivations for a better understanding of their structure is that they show up naturally in connection with Remeslennikov's conjecture on the profinite rigidity of free groups. In this article, we determine when the fundamental group of a finite graph of groups with cyclic edge groups is parafree.

On the Drinfeld formal group
Deven Manam
https://arxiv.org/abs/2403.02555 https://arxiv.org/pdf/2403.02555

On the Drinfeld formal group
We identify Drinfeld's formal group on the prismatization of $\mathrm{Spf}\,\mathbb{Z}_p$ with a formal group arising from homotopy theory, given locally by the Quillen formal group of a decompleted variant of topological periodic cyclic homology. We also prove that this formal group extends to the syntomization of $\mathrm{Spf}\,\mathbb{Z}_p$, and that it admits a certain algebraization conjectured by Drinfeld.

This https://arxiv.org/abs/2306.03260 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A cyclic random motion in $\mathbb{R}^3$ driven by geometric counting processes
We consider the random motion of a particle that moves with constant velocity in $\mathbb{R}^3$. The particle can move along four directions with different speeds that are attained cyclically. It follows that the support of the stochastic process describing the particle's position at time $t$ is a tetrahedron. We assume that the sequence of sojourn times along each direction follows a geometric counting process (GCP). When the initial velocity is fixed, we obtain the explicit form of the probab…

Stable Graded Multiplicities for Harmonics on a Cyclic Quiver
Andrew Frohmader, Alexander Heaton
https://arxiv.org/abs/2402.16198 https://

Stable Graded Multiplicities for Harmonics on a Cyclic Quiver
We consider Vinberg $θ$-groups associated to a cyclic quiver on $k$ nodes. Let $K$ be the product of the general linear groups associated to each node. Then $K$ acts naturally on $\oplus \text{Hom}(V_i, V_{i+1})$ and by Vinberg's theory the polynomials are free over the invariants. We therefore consider the harmonics as a representation of $K$, and give a combinatorial formula for the stable graded multiplicity of each $K$-type. A key lemma provides a combinatorial separation of variables that…

Efficient Calculations for k-diagonal Circulant Matrices and Cyclic Banded Matrices
Chen Wang, Chao Wang
https://arxiv.org/abs/2403.05048 https://

Efficient Calculations for k-diagonal Circulant Matrices and Cyclic Banded Matrices
Calculating the inverse of $k$-diagonal circulant matrices and cyclic banded matrices is a more challenging problem than calculating their determinants. Algorithms that directly involve or specify linear or quadratic complexity for the inverses of these two types of matrices are rare. This paper presents two fast algorithms that can compute the complexity of a $k$-diagonal circulant matrix within complexity $O(k^3 \log n+k^4)+kn$, and for $k$-diagonal cyclic banded matrices it is $O(k^3 n+k^5)+…

This https://arxiv.org/abs/2304.13496 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

An Improved Modular Addition Checksum Algorithm
This paper introduces a checksum algorithm that provides a new point in the performance/complexity/effectiveness checksum tradeoff space. It has better fault detection properties than single-sum and dual-sum modular addition checksums. It is also simpler to compute efficiently than a cyclic redundancy check (CRC) due to exploiting commonly available hardware and programming language support for unsigned integer division. The key idea is to compute a single running sum, but introduce a left shif…

Self-organised dynamics beyond scaling of avalanches: Cyclic stress fluctuations in critical sandpiles
Bosiljka Tadic, Alexander Shapoval, Mikhail Shnirman
https://arxiv.org/abs/2403.15859

Self-organised dynamics beyond scaling of avalanches: Cyclic stress fluctuations in critical sandpiles
Recognising changes in collective dynamics in complex systems is essential for predicting potential events and their development. Possessing intrinsic attractors with laws associated with scale invariance, self-organised critical dynamics represent a suitable example for quantitatively studying changes in collective behaviour. We consider two prototypal models of self-organised criticality, the sandpile automata with deterministic (Bak-Tang-Wiesenfeld) and probabilistic (Manna model) dynamical …

Cyclic sieving on permutations -- an analysis of maps and statistics in the FindStat database
Ashleigh Adams, Jennifer Elder, Nadia Lafreni\`ere, Erin McNicholas, Jessica Striker, Amanda Welch
https://arxiv.org/abs/2402.16251

Cyclic sieving on permutations -- an analysis of maps and statistics in the FindStat database
We perform a systematic study of permutation statistics and bijective maps on permutations using SageMath to search the FindStat combinatorial statistics database to identify apparent instances of the cyclic sieving phenomenon (CSP). Cyclic sieving occurs on a set of objects, a statistic, and a map of order $n$ when the evaluation of the statistic generating function at the $d$th power of the primitive $n$th root of unity equals the number of fixed points under the $d$th power of the map. Of th…

This https://arxiv.org/abs/2205.13436 has been replaced.
link: https://scholar.google.com/scholar?q=a

The cyclic open-closed map, u-connections and R-matrices
This paper considers the (negative) cyclic open-closed map $\mathcal{OC}^{-}$, which maps the cyclic homology of the Fukaya category of a symplectic manifold to its $S^1$-equivariant quantum cohomology. We prove (under simplifying technical hypotheses) that this map respects the respective natural connections in the direction of the equivariant parameter. In the monotone setting this allows us to conclude that $\mathcal{OC}^{-}$ intertwines the decomposition of the Fukaya category by eigenvalue…

Discrete iterated integrals and cyclic sum formulas
Hanamichi Kawamura
https://arxiv.org/abs/2404.16161 https://arxiv.org/pdf/2404.16…

Discrete iterated integrals and cyclic sum formulas
In this paper, we consider a discrete version of iterated integrals by the naive (equally divided) Riemann sum. In particular, basic three formulas for usual iterated integrals are discritized. Moreover, we proved cyclic sum formulas for discrete iterated integrals. They imply the cyclic sum formula for multiple polylogarithms.

Distributional Topological Complexity of groups
Alexander Dranishnikov
https://arxiv.org/abs/2404.03041 https://arxiv.org/pdf/2404.03…

Distributional Topological Complexity of groups
We study numerical invariants $d\TC(Γ)$ and $d\cat(Γ)$ of groups recently introduced in \cite{DJ} and independently in \cite{KW}. We compute $d\TC$ for finite cyclic groups $\mathbb Z_p$ with prime $p$ as well as for nonorientable surfaces of genus $g>3$ (for orientable surfaces it was computed in \cite{DJ}). We prove the formula $$d\TC(G\ast H)=\max\{d\TC (G),d\TC (H), \cd(G\times H)\}$$ for torsion free groups.

On the Existence of Cyclic Lattice Codes
Chengpin Luo, Brian M. Kurkoski
https://arxiv.org/abs/2402.18094 https://arxiv.org/pdf/2402.…

On the Existence of Cyclic Lattice Codes
A coding lattice $Λ_c$ and a shaping lattice $Λ_s$ forms a nested lattice code $\mathcal{C}$ if $Λ_s \subseteq Λ_c$. Under some conditions, $\mathcal{C}$ is a finite cyclic group formed by rectangular encoding. This paper presents the conditions for the existence of such $\mathcal{C}$ and provides some designs. These designs correspond to solutions to linear Diophantine equations so that a cyclic lattice code $\mathcal C$ of arbitrary codebook size $M$ can possess group isomorphism, which i…

This https://arxiv.org/abs/2404.00499 has been replaced.
link: https://scholar.google.com/scholar?q=a

On Faddeev's Equation
Faddeev' equations are a set-theoretical and an operator forms of the star-triangle equation. Known solutions of the quantum star-triangle equation, related to the Faddeev equations, are based on various forms of the modular double of the Weyl algebra including its cyclic representation. We show in this paper that Fadeev's equation also leads to a solution of the quantum star-triangle equation even in the case of a simple Weyl algebra with $|q|<1$. This paper can be seen as an addendu…

Cyclic operads through modules
Thomas Willwacher
https://arxiv.org/abs/2403.18399 https://arxiv.org/pdf/2403.18399

Cyclic operads through modules
We describe a way to compute mapping spaces of cyclic operads through modules. As an application we compute the homotopy automorphism space of the cyclic Batalin-Vilkovisky (Hopf co-)operad.

Primitive elements in the Hall algebra of a cyclic quiver
Renda Ma
https://arxiv.org/abs/2403.18065 https://arxiv.org/pdf/2403.18065<…

Primitive elements in the Hall algebra of a cyclic quiver
We provide an explicit formula for primitive elements in the Hall algebras of nilpotent representations of cyclic quivers.

This https://arxiv.org/abs/1904.02310 has been replaced.
link: https://scholar.google.com/scholar?q=a

Steiner systems $S(2,4,2^m)$ supported by a family of extended cyclic codes
In [C. Ding, An infinite family of Steiner systems $S(2,4,2^m)$ from cyclic codes, {\em J. Combin. Des.} 26 (2018), no.3, 126--144], Ding constructed a family of Steiner systems $S(2,4,2^m)$ for all $m \equiv 2 \pmod{4}$ from a family of extended cyclic codes. The objective of this paper is to present a family of Steiner systems $S(2,4,2^m)$ for all $m \equiv 0 \pmod{4}$ supported by a family of extended cyclic codes. The main result of this paper complements the previous work of Ding, and the …

This https://arxiv.org/abs/2404.16161 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Discrete iterated integrals and cyclic sum formulas
In this paper, we consider a discrete version of iterated integrals by the naive (equally divided) Riemann sum. In particular, basic three formulas for usual iterated integrals are discritized. Moreover, we proved cyclic sum formulas for discrete iterated integrals. They imply the cyclic sum formula for multiple polylogarithms.

Diagramatics for cyclic pointed fusion categories
Agustina Czenky
https://arxiv.org/abs/2404.08084 https://arxiv.org/pdf/2404.08084…

Diagramatics for cyclic pointed fusion categories
We give a parametrization of cyclic pointed categories associated to the cyclic group of order $n$ in terms of $n$-th roots of unity. We also provide a diagramatic description of these categories by generators and relations, and use it to characterize their $2$-group of automorphisms.

Effective Categorical Enumerative Invariants
Andrei Caldararu, Junwu Tu
https://arxiv.org/abs/2404.01499 https://arxiv.org/pdf/2404.0…

Effective Categorical Enumerative Invariants
We introduce enumerative invariants $F_{g,n}$ $(g\geq0$, $n \geq 1)$ associated to a cyclic $A_\infty$ algebra and a splitting of its non-commutative Hodge filtration. These invariants are defined by explicitly computable Feynman sums, and encode the same information as Costello's partition function of the corresponding field theory. Our invariants are stable under Morita equivalence, and therefore can be associated to a Calabi-Yau category with splitting data. This justifies the name categor…

Some bounds on the cardinality of the $b$-symbol weight spectrum of codes
Hongwei Zhu, Shitao Li, Minjia Shi, Shu-Tao Xia, Patrick Sole
https://arxiv.org/abs/2404.02471

Some bounds on the cardinality of the $b$-symbol weight spectrum of codes
The size of the Hamming distance spectrum of a code has received great attention in recent research. The main objective of this paper is to extend these significant theories to the $b$-symbol distance spectrum. We examine this question for various types of codes, including unrestricted codes, additive codes, linear codes, and cyclic codes, successively. For the first three cases, we determine the maximum size of the $b$-symbol distance spectra of these codes smoothly. For the case of cyclic cod…

Hilbert spaces over $C^*$-tensor categories, Fredholm modules and cyclic cohomology
Abhishek Banerjee, Subhajit Das, Surjeet Kour
https://arxiv.org/abs/2404.15162

Hilbert spaces over $C^*$-tensor categories, Fredholm modules and cyclic cohomology
We construct Fredholm modules over an algebra taking values in generalized Hilbert spaces over a rigid $C^*$-tensor category. Using methods of Connes, we obtain Chern characters taking values in cyclic cohomology. These Chern characters are well behaved with respect to the periodicity operator, and depend only on the homotopy class of the Fredholm module.

Primitive elements in the Hall algebra of a cyclic quiver
Renda Ma
https://arxiv.org/abs/2403.18065 https://arxiv.org/pdf/2403.18065<…

Primitive elements in the Hall algebra of a cyclic quiver
We provide an explicit formula for primitive elements in the Hall algebras of nilpotent representations of cyclic quivers.

Quantum charges of harmonic oscillators
Alexander D. Popov
https://arxiv.org/abs/2404.01756 https://arxiv.org/pdf/2404.01756

Quantum charges of harmonic oscillators
We discuss Riemannian geometry of one-dimensional quantum harmonic oscillator. Its wavefunction is a holomorphic section of the complex line bundle $L_{\sf{v}}$ over the phase space $\mathbb{R}^2$. We show that the energy eigenfunctions $ψ_n$ with $n\ge 1$, corresponding to the energy levels $E_n$, are complex coordinates on orbifolds $\mathbb{R}^2/\mathbb{Z}_n$ embedded into $L_{\sf{v}}$, where $\mathbb{Z}_n$ is the cyclic group of order $n$. In fact, $ψ_n (t,z)$ is a standing wave on $\math…

Effective Categorical Enumerative Invariants
Andrei Caldararu, Junwu Tu
https://arxiv.org/abs/2404.01499 https://arxiv.org/pdf/2404.0…

Effective Categorical Enumerative Invariants
We introduce enumerative invariants $F_{g,n}$ $(g\geq0$, $n \geq 1)$ associated to a cyclic $A_\infty$ algebra and a splitting of its non-commutative Hodge filtration. These invariants are defined by explicitly computable Feynman sums, and encode the same information as Costello's partition function of the corresponding field theory. Our invariants are stable under Morita equivalence, and therefore can be associated to a Calabi-Yau category with splitting data. This justifies the name categor…

This https://arxiv.org/abs/2311.09314 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multimatroids and rational curves with cyclic action
We study the connection between multimatroids and moduli spaces of rational curves with cyclic action. Multimatroids are generalizations of matroids and delta-matroids introduced by Bouchet, which naturally arise in topological graph theory. The vantage point of moduli of curves provides a tropical framework for studying multimatroids, generalizing the previous connection between type-A permutohedral varieties (Losev--Manin moduli spaces) and matroids, and the connection between type-B permutoh…

Diagramatics for cyclic pointed fusion categories
Agustina Czenky
https://arxiv.org/abs/2404.08084 https://arxiv.org/pdf/2404.08084…

Diagramatics for cyclic pointed fusion categories
We give a parametrization of cyclic pointed categories associated to the cyclic group of order $n$ in terms of $n$-th roots of unity. We also provide a diagramatic description of these categories by generators and relations, and use it to characterize their $2$-group of automorphisms.

This https://arxiv.org/abs/2303.13728 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Kervaire conjecture on weight of group via fundamental group of ribbon sphere-link
Kervaire conjecture that the weight of the free product of every non-trivial group and the infinite cyclic group is not one is confirmed by confirming Conjecture Z of a knot exterior.

The multiplicity of cyclic coverings of a singularity of an algebraic variety
Toya Kumagai, Tomohiro Okuma
https://arxiv.org/abs/2403.14355 https://…

The multiplicity of cyclic coverings of a singularity of an algebraic variety
Let $V$ be an affine algebraic variety, and let $p\in V$ be a singular point. For a regular function $g$ on $V$ such that $g(p)=0$ and for a positive integer $n$, we consider the cyclic covering $ϕ_n\: V_n \to V$ of degree $n$ branched along the hypersurface defined by $g$. We will prove that for sufficiently large $n$, the tangent cone of $V_n$ at $ϕ_n^{-1}(p)$ is, as an affine variety, the product of the tangent cone of the branch locus and the affine line. In particular, the multiplicity o…

On a bijection between a finite group to a non-cyclic group with divisibility of element orders
Mohsen Amiri
https://arxiv.org/abs/2402.13247 https://

On a bijection between a finite group to a non-cyclic group with divisibility of element orders
Consider a finite group $G$ of order $n$ with a prime divisor $p$. In this article, we establish, among other results, that if the Sylow $p$-subgroup of $G$ is neither cyclic nor generalized quaternion, then there exists a bijection $f$ from $G$ onto the abelian group $C_{\frac{n}{p}}\times C_p$ such that for every element $x$ in $G$, the order of $x$ divides the order of $f(x)$. This resolves Question 1.5 posed in [12].

Two bijections in the spirit of the transformation fondamentale
Umesh Shankar
https://arxiv.org/abs/2404.01788 https://arxiv.org/pdf/…

Two bijections in the spirit of the transformation fondamentale
In this short paper, we give bijective proofs of two recent equidistribution results connecting cyclic and linear statistics in the spirit of the Foata's ``transformation fondamentale''.

This https://arxiv.org/abs/2404.06464 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Hasse norm principle for 3-manifolds in arithmetic topology
Following the analogies between knots and primes, 3-manifolds and number rings in arithmetic topology, we show a topological analogue of the Hasse norm principle for finite cyclic coverings of 3-manifolds, which was originally stated for finite cyclic extensions of number fields.

Cyclic wide subalgebras of semisimple Lie algebras
Andrew Douglas, Joe Repka
https://arxiv.org/abs/2404.07372 https://arxiv.org/pdf/2…

Cyclic wide subalgebras of semisimple Lie algebras
Let $\mathfrak{s}$ $\ltimes$ $\mathfrak{r}$ be a Levi decomposable Lie algebra, with Levi factor $\mathfrak{s}$, and radical $\mathfrak{r}$. A module $V$ of $\mathfrak{s}$ $\ltimes$ $\mathfrak{r}$ is cyclic indecomposable if it is indecomposable and the quotient module $V /\mathfrak{r}\cdot V$ is a simple $\mathfrak{s}$-module. A Levi decomposable subalgebra of a semisimple Lie algebra is cyclic wide if the restriction of every simple module of the semisimple Lie algebra to the subalgebra is cy…

This https://arxiv.org/abs/2307.01627 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Noncoprime action of a cyclic group
Let $A$ be a finite nilpotent group acting fixed point freely on the finite (solvable) group $G$ by automorphisms. It is conjectured that the nilpotent length of $G$ is bounded above by $\ell(A)$, the number of primes dividing the order of $A$ counted with multiplicities. In the present paper we consider the case $A$ is cyclic and obtain that the nilpotent length of $G$ is at most $2\ell(A)$ if $|G|$ is odd. More generally we prove that the nilpotent length of $G$ is at most $2\ell(A)…

Token graphs of Cayley graphs as lifts
C. Dalf\'o, M. A. Fiol, S. Pavl\'ikov\'a, J. \v{S}ir\'a\v{n}
https://arxiv.org/abs/2404.02122 https:…

Token graphs of Cayley graphs as lifts
This paper describes a general method for representing $k$-token graphs of Cayley graphs as lifts of voltage graphs. This allows us to construct line graphs of circulant graphs and Johnson graphs as lift graphs on cyclic groups. As an application of the method, we derive the spectra of the considered token graphs. This method can also be applied to dealing with other matrices, such as the Laplacian or the signless Laplacian, and to construct token digraphs of Cayley digraphs.

This https://arxiv.org/abs/2401.04885 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Cyclic and Negacyclic Sum-Rank Codes
Sum-rank codes have known applications in the multishot network coding, the distributed storage and the construction of space-time codes. U. Mart\'ınez-Peñas introduced the cyclic-skew-cyclic sum-rank codes and proposed the BCH bound on the cyclic-skew-cyclic sum-rank codes in his paper published in IEEE Trans. Inf. Theory, vol. 67, no. 8, 2021. Afterwards, many sum-rank BCH codes with lower bounds on their dimensions and minimum sum-rank distances were constructed. Sum-rank Hartmann-Tzeng bo…

The sandpile model on the complete split graph: $q,t$-Schr\"oder polynomials, sawtooth polyominoes, and a cyclic lemma
Henri Derycke, Mark Dukes, Yvan Le Borgne
https://arxiv.org/abs/2402.15372

The sandpile model on the complete split graph: $q,t$-Schröder polynomials, sawtooth polyominoes, and a cyclic lemma
This paper builds on work initiated in Dukes (2021) that considered the classification of recurrent configurations of the Abelian sandpile model on the complete split graph. We introduce two statistics, wtopple$_{CTI}$ and wtopple$_{ITC}$, on sorted recurrent configurations. These statistics arise from two natural but different toppling conventions, CTI and ITC, for Dhar's burning algorithm as it is applied to the complete split graph. In addition, we introduce the bivariate $q,t$-CTI and $q,t$…

Extended genus fields of abelian extensions of rational function fields
Juan Carlos Hernandez-Bocanegra, Gabriel Villa-Salvador
https://arxiv.org/abs/2404.17566

Extended genus fields of abelian extensions of rational function fields
In this paper we obtain the extended genus field of a finite abelian extension of a global rational function field. We first study the case of a cyclic extension of prime power degree. Next, we use that the extended genus fields of a composite of two cyclotomic extensions of a global rational function field is equal to the composite of their respective extended genus fields, to obtain our main result. This result is that the extended genus field of a general finite abelian extension of a global…

This https://arxiv.org/abs/2401.04885 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Cyclic and Negacyclic Sum-Rank Codes
Sum-rank codes have known applications in the multishot network coding, the distributed storage and the construction of space-time codes. U. Mart\'ınez-Peñas introduced the cyclic-skew-cyclic sum-rank codes and proposed the BCH bound on the cyclic-skew-cyclic sum-rank codes in his paper published in IEEE Trans. Inf. Theory, vol. 67, no. 8, 2021. Afterwards, many sum-rank BCH codes with lower bounds on their dimensions and minimum sum-rank distances were constructed. Sum-rank Hartmann-Tzeng bo…

Exact bounds for the sum of the inverse-power of element orders in non-cyclic finite groups
M. Archita
https://arxiv.org/abs/2404.07500 https://

Exact bounds for the sum of the inverse-power of element orders in non-cyclic finite groups
Given a finite group $G$ of order $n.$ Denote the sum of the inverse-power of element orders in $G$ by $m(G).$ Let $\mathbb{Z}_n$ be the cyclic group of order $n.$ Suppose $G$ is a non-cyclic group of order $n$ then we show that $m(G)\geq \frac{5}{4}m(\mathbb{Z}_n).$ Our result improves the inequality $m(G)>m(\mathbb{Z}_n)$ obtained by Baniasad Azad, M., and Khorsravi B. Moreover, this bound is best as for $n=4l, l$ odd, there exists a group $G$ of order $n$ satisfying $m(G)=\frac{5}{4}m(\mathb…

This https://arxiv.org/abs/2401.06184 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Cyclic and Negacyclic Codes with Optimal and Best Known Minimum Distances
In this paper, we construct a new family of distance-optimal binary cyclic codes with the minimum distance $6$ and a new family of distance-optimal quaternary cyclic codes with the minimum distance $4$. We also construct several families of cyclic and negacyclic codes over ${\bf F}_2$, ${\bf F}_3$, ${\bf F}_4$, ${\bf F}_5$, ${\bf F}_7$ and ${\bf F}_9$ with good parameters $n,\,k,\,d$, such that the maximal possible minimum distance $d_{max}$ of a linear $[n, k]_q$ code is at most $d_{max} \leq …

Descent for projective twists of modular curves
Franciszek Knyszewski
https://arxiv.org/abs/2402.17636 https://arxiv.org/pdf/2402.176…

Descent for projective twists of modular curves
Let $F$ be a number field and $p\geq7$ a rational prime. We obtain a simple descent criterion characterising those projective Galois representations $\overlineρ:G_F\to\mathrm{PGL}_2(\mathbb{F}_p)$ for which the corresponding twist $X_{\overlineρ}(p)$ of the principal modular curve of level $p$ is defined over $\mathbb{Q}$. We also give a more concrete version of this result for representations which arise from elliptic curves over cyclic number fields.

All bipartite circulants are dispersable
Shannon Overbay, Samuel Joslin, Paul C. Kainen
https://arxiv.org/abs/2404.19200 https://arxi…

All bipartite circulants are dispersable
We show that a cyclic vertex order due to Yu, Shao and Li gives a dispersable book embedding for any bipartite circulant.

This https://arxiv.org/abs/2403.14894 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the discrete trajectories of a self-propelled particle
We introduce a double-folded operator that, upon iterative application, generates a dynamical system with two types of trajectories: a cyclic one and, another that grows endlessly on parabolas. These trajectories produce two distinct partitions of the set of lattice points in the plane. Our object is to analyze these trajectories and to point out a few special arithmetic properties of the integers they represent. We also introduce and study the parabolic-taxicab distance, which measures the…

The "spread" of Thompson's group $F$
Gili Golan
https://arxiv.org/abs/2402.19444 https://arxiv.org/pdf/2402.19444

The "spread" of Thompson's group $F$
Recall that a group $G$ is said to be $\frac{3}{2}$-generated if every non-trivial element $g\in G$ has a co-generator in $G$ (i.e., an element which together with $g$ generates $G$). Thompson's group $V$ was proved to be $\frac{3}{2}$-generated by Donoven and Harper in 2019. It was the first example of an infinite finitely presented non-cyclic $\frac{3}{2}$-generated group. In 2022, Bleak, Harper and Skipper proved that Thompson's group $T$ is also $\frac{3}{2}$-generated. Since the abelianiza…

This https://arxiv.org/abs/2209.10858 has been replaced.
link: https://scholar.google.com/scholar?q=a

Normal integral bases of Lehmer's cyclic quintic fields
Let $K_n$ be a tamely ramified cyclic quintic field generated by a root of Emma Lehmer's parametric polynomial. We give all normal integral bases for $K_n$ only by the roots of the polynomial, which is a generalization of the work of Lehmer in the case that $n^4+5n^3+15n^2+25n+25$ is prime number, and Spearman-Willliams in the case that $n^4+5n^3+15n^2+25n+25$ is square-free.

Binary Cyclic Transversal Polytopes
Jonas Frede, Volker Kaibel, Maximilian Merkert
https://arxiv.org/abs/2404.06088 https://arxiv.org…

Binary Cyclic Transversal Polytopes
With every family of finitely many subsets of a finite-dimensional vector space over the Galois-field with two elements we associate a cyclic transversal polytope. It turns out that those polytopes generalize several well-known polytopes that are relevant in combinatorial optimization, among them cut polytopes as well as stable set and matching polytopes. We introduce the class of lifted odd-set inequalities and prove results demonstrating their strength. In particular, we show that they suffic…

This https://arxiv.org/abs/2205.11421 has been replaced.
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Transference for loose Hamilton cycles in random $3$-uniform hypergraphs
A loose Hamilton cycle in a hypergraph is a cyclic sequence of edges covering all vertices in which only every two consecutive edges intersect and do so in exactly one vertex. With Dirac's theorem in mind, it is natural to ask what minimum $d$-degree condition guarantees the existence of a loose Hamilton cycle in a $k$-uniform hypergraph. For $k=3$ and each $d \in \{1,2\}$, the necessary and sufficient such condition is known precisely. We show that these results adhere to a `transference princ…