Tootfinder

PSPACE-completeness of bimodal transitive weak-density logic
Philippe Balbiani, Olivier Gasquet
https://arxiv.org/abs/2507.14949 https://

PSPACE-completeness of bimodal transitive weak-density logic
Windows have been introduce in \cite{BalGasq25} as a tool for designing polynomial algorithms to check satisfiability of a bimodal logic of weak-density. In this paper, after revisiting the ``folklore'' case of bimodal $\K4$ already treated in \cite{Halpern} but which is worth a fresh review, we show that windows allow to polynomially solve the satisfiability problem when adding transitivity to weak-density, by mixing algorithms for bimodal K together with windows-approach. The conclusion is th…

TIL it's a verb (Wiktionary)
Verb
lint (third-person singular simple present lints, present participle linting, simple past and past participle linted)
(transitive, computing) To perform a static check on (source code) to detect stylistic or programmatic errors.
You should lint your JavaScript code before committing it.

Non-split sharply 2-transitive groups of bounded exponent
Marco Amelio
https://arxiv.org/abs/2509.11958 https://arxiv.org/pdf/2509.11958

Non-split sharply 2-transitive groups of bounded exponent
We construct here the first known examples of non-split sharply 2-transitive groups of bounded exponent in odd positive characteristic for every large enough prime $p \equiv 3 \pmod{4}$. In fact, we show that there are countably many pairwise non-isomorphic countable non-split sharply 2-transitive groups of characteristic $p$ for each such $p$. Furthermore, we construct non-periodic non-split sharply 2-transitive groups (of these same characteristics) with centralizers of involutions of bounded…

Spanning Factorizations in Vertex-Transitive Digraphs of Degree 2
Vance Faber
https://arxiv.org/abs/2509.13432 https://arxiv.org/pdf/2509.13432

Spanning Factorizations in Vertex-Transitive Digraphs of Degree 2
We investigate spanning 1-factorizations in vertex-transitive digraphs of arbitrary out-degree d. The guiding question is whether every such digraph admits a spanning 1-factorization that includes, for each vertex v, all d out-edges (v, F1(v)) from v. Equivalently, does there always exist a spanning factorization containing the empty word together with the full set of generators {F1, ..., Fd}? This paper addresses the case d = 2. Using the structure of alternating cycles and block systems, we…

Replaced article(s) found for math.FA. https://arxiv.org/list/math.FA/new
[1/1]:
- Doubly transitive equiangular tight frames that contain regular simplices
Matthew Fickus, Evan C. Lake

Faster Multi-Source Reachability and Approximate Distances via Shortcuts, Hopsets and Matrix Multiplication
Michael Elkin, Chhaya Trehan
https://arxiv.org/abs/2507.13470

Faster Multi-Source Reachability and Approximate Distances via Shortcuts, Hopsets and Matrix Multiplication
Given an $n$-vertex $m$-edge digraph $G = (V,E)$ and a subset $S \subseteq V$ of $|S| = n^σ$ (for some $0 \le σ\le 1$) designated sources, the $S \times V$ reachability problem is to compute the sets $\mathcal V_s$ of vertices reachable from $s$, for every $s \in S$. Naive centralized algorithms run BFS/DFS from each source in $O(m \cdot n^σ)$ time or compute $G$'s transitive closure in $\hat O(n^ω)$ time, where $ω\le 2.371552\ldots$ is the matrix multiplication exponent. Thus, t…

A coarse Halin Grid Theorem with applications to quasi-transitive, locally finite graphs
Sandra Albrechtsen, Matthias Hamann
https://arxiv.org/abs/2507.12973

A coarse Halin Grid Theorem with applications to quasi-transitive, locally finite graphs
We prove a coarse version of Halin's Grid Theorem: Every one-ended, locally finite graph that contains the disjoint union of infinitely many rays as an asymptotic minor also contains the half-grid as an asymptotic minor. More generally, we show that the same holds for arbitrary (not necessarily one-ended or locally finite) graphs under additional, necessary assumptions on the minor-models of the infinite rays. This resolves a conjecture of Georgakopoulos and Papasoglu. As an application, we s…

Comparing transitive dependency version resolution in #Rust and #Java
https://blog.frankel.ch/dependency-ver

On the structure of braces whose subideals are ideals
Martyn R. Dixon, Leonid A. Kurdachenko, Igor Ya. Subbotin
https://arxiv.org/abs/2508.13133 https://ar…

On the structure of braces whose subideals are ideals
This article begins the study of T-braces, those skew left braces of abelian type in which the relation of being an ideal is a transitive relation.

Self-propulsion via non-transitive phase coexistence in chemically active mixtures
Yicheng Qiang, Chengjie Luo, David Zwicker
https://arxiv.org/abs/2508.09816 https://

Self-propulsion via non-transitive phase coexistence in chemically active mixtures
Phase separation drives the formation of biomolecular condensates in cells, which comprise many components and sometimes possess multiple phases. The equilibrium physics of phase separation is well understood, but many components in condensates undergo active reactions. We demonstrate that such reactions affect phase separation by altering the chemical potential balance and by introducing an osmotic pressure difference at interfaces. However, the system does not permit a pseudo-pressure balance…

Embeddings into highly transitive and mixed identity free groups
James Hyde, Yash Lodha
https://arxiv.org/abs/2509.09788 https://arxiv.org/pdf/2509.09788…

Embeddings into highly transitive and mixed identity free groups
Given a countable group $G$, we develop a method to construct an overgroup $H$ that is finitely generated, highly transitive and mixed identity free. Our construction can be controlled to ensure that some fundamental group theoretic properties of $G$ are inherited by $H$, such as amenability or the property of not containing a nonabelian free group. The former provides a strong solution to a question of Hull and Osin, and the latter provides the first examples of nonamenable groups without free…

Gathering in Non-Vertex-Transitive Graphs Under Round Robin
Serafino Cicerone, Alessia Di Fonso, Gabriele Di Stefano, Alfredo Navarra
https://arxiv.org/abs/2509.06064 https://…

Gathering in Non-Vertex-Transitive Graphs Under Round Robin
The Gathering problem for a swarm of robots asks for a distributed algorithm that brings such entities to a common place, not known in advance. We consider the well-known OBLOT model with robots constrained to move along the edges of a graph, hence gathering in one vertex, eventually. Despite the classical setting under which the problem has been usually approached, we consider the `hostile' case where: i) the initial configuration may contain multiplicities, i.e. more than one robot may occupy…

On transitive and homogeneous binary $G$-spaces
Pavel S. Gevorgyan, Quitzeh Morales Melendez
https://arxiv.org/abs/2509.05847 https://arxiv.org/pdf/2509.05…

On transitive and homogeneous binary $G$-spaces
In this paper, the notions of transitivity and homogeneity in binary $G$-spaces are studied. These notions coincide for distributive binary $G$-spaces. For compact $G$, it is shown that distributive transitive binary $G$-spaces are coset spaces with a suitably defined binary $G$-action. Homogeneous binary $G$-spaces are topologically homogeneous and are separated into distinct stabilization types. Examples of each type are constructed.

Zero Forcing on Iterated Graph Models
Christopher Brice, Erin Meger, Nhat-Dinh Nguyen, Allen Rakhamimov, Abigail Raz
https://arxiv.org/abs/2507.12579 https…

Zero Forcing on Iterated Graph Models
Modeling how information travels throughout a network has vast applications across social sciences, cybersecurity, and graph-based neural networks. In this paper, we consider the zero forcing model for information diffusion on iterative deterministic complex network models. In particular, we continue the exploration of the Iterative Local Transitive (ILT) model and the Iterative Local Anti-Transitive (ILAT) model, both introduced by Bonato et. al. in 2009 and 2017, respectively. These models us…

Quantum symmetry of $3$-transitive graphs
Simon Schmidt, Makoto Yamashita
https://arxiv.org/abs/2508.02562 https://arxiv.org/pdf/2508.02562

Quantum symmetry of $3$-transitive graphs
We study the quantum automorphism group of $3$-transitive graphs in this article. Those are highly symmetric graphs that were classified by Cameron and Macpherson in 1985, and we compute the quantum automorphism group of all such graphs, excluding the orthogonal graphs $\mathrm{O}^-(6,q)$ for $q>3$. We show that there is no quantum symmetry for the McLaughlin graph and the orthogonal graphs $\mathrm{O}^-(6,q)$ with $q = 2, 3$, while that the quantum automorphism group of the affine polar graphs…

The distribution of symmetry of Lorentzian naturally reductive nilmanifolds
Brian Luporini, Silvio Reggiani, Francisco Vittone
https://arxiv.org/abs/2509.10622 https://

The distribution of symmetry of Lorentzian naturally reductive nilmanifolds
We study $2$-step nilpotent Lorentzian Lie groups $N$, which are naturally reductive with respect to a certain class of transitive subgroups of isometries. We describe the isotropy representation and prove that its fixed points give raise to the distribution of symmetry of $N$. This generalizes some known results for the Riemannian case.

On two-distance-transitive graphs
Wei Jin, Jack H. Koolen, Chenhui Lv
https://arxiv.org/abs/2508.02010 https://arxiv.org/pdf/2508.02010

On two-distance-transitive graphs
A $2$-distance-transitive graph is a vertex-transitive graph whose vertex stabilizer is transitive on both the first step and the second step neighborhoods. In this paper, we first answer a question of A. Devillers, M. Giudici, C. H. Li and C. E. Praeger in 2012 about vertex-quasiprimitive $2$-distance-transitive graphs for the odd order case. Then we characterize $2$-distance-transitive graphs of valency $p$ or $p+1$ where $p$ is a prime. After that, as an application of the above result, we c…

Characterization of Ergodic Measures of Maximal Entropy for Topologically Transitive Partially Hyperbolic Diffeomorphisms with compact center leaves
Jorge Crisostomo, Richard Cubas
https://arxiv.org/abs/2507.23081

Characterization of Ergodic Measures of Maximal Entropy for Topologically Transitive Partially Hyperbolic Diffeomorphisms with compact center leaves
In this paper, we provide an upper bound on the number of maximal entropy ergodic measures with zero Lyapunov exponent for topologically transitive partially hyperbolic diffeomorphisms with compact one-dimensional center leaves on $\mathbb{T}^3$. Furthermore, we establish a comprehensive characterization of the support of these measures.

Guarded Fragments Meet Dynamic Logic: The Story of Regular Guards (Extended Version)
Bartosz Bednarczyk, Emanuel Kiero\'nski
https://arxiv.org/abs/2509.09218 https://…

Guarded Fragments Meet Dynamic Logic: The Story of Regular Guards (Extended Version)
We study the Guarded Fragment with Regular Guards (RGF), which combines the expressive power of the Guarded Fragment (GF) with Propositional Dynamic Logic with Intersection and Converse (ICPDL). Our logic generalizes, in a uniform way, many previously-studied extensions of GF, including (conjunctions of) transitive or equivalence guards, transitive or equivalence closure and more. We prove 2EXPTIME-completeness of the satisfiability problem for RGF, showing that RGF is not harder than ICPDL or …

Heavy repulsion of clusters in Bernoulli percolation
Sasha Bell, Tasmin Chu, Owen Rodgers, Grigory Terlov, Anush Tserunyan
https://arxiv.org/abs/2509.10631 https://

Heavy repulsion of clusters in Bernoulli percolation
We study Bernoulli$(p)$ percolation on (non)unimodular quasi-transitive graphs and prove that, almost surely, for any two heavy clusters $C$ and $C'$, the set of vertices in $C$ within distance one of $C'$ is light, i.e. it has finite total weight. This is a significant step towards resolving a longstanding question posed by Häggström, Peres, and Schonmann, and a generalization of a theorem of Timár, who proved the same result in the unimodular setting. Our proof adapts Timár's approach but…

Ramsey-like theorems for separable permutations
Quentin Le Hou\'erou, Ludovic Patey
https://arxiv.org/abs/2507.07606 https://arxi…

Ramsey-like theorems for separable permutations
We conduct a computability-theoretic study of Ramsey-like theorems of the form "Every coloring of the edges of an infinite clique admits an infinite sub-clique avoiding some pattern", with a particular focus on transitive patterns. As it turns out, the patterns corresponding to separable permutations play an important role in the computational features of the statement. We prove that the avoidance of any separable permutation is equivalent to the existence of an infinite homogeneous set in stan…

From Age-Structured Trophic Networks to Applied Control : Stabilization and Harvesting Strategies for Non-Transitive Competition and the Dynamics of Mosquitoes
Marius Bargo, Yacouba Simpore
https://arxiv.org/abs/2509.02704

From Age-Structured Trophic Networks to Applied Control : Stabilization and Harvesting Strategies for Non-Transitive Competition and the Dynamics of Mosquitoes
We propose and analyze a nonlinear age-structured multi-species model that serves as a unifying framework for ecological and biotechnological systems in complex environments (microbial communities, bioreactors, etc.). The formulation incorporates nonlocal intra- and interspecific interactions modulated by environmental covariates; under general assumptions on mortality, reproduction rates and interaction kernels, we establish existence, uniqueness and positivity of solutions. We illustrate the …

On cubic vertex-transitive graphs of given girth
Ted Dobson, Ademir Hujdurovi\'c, Wilfried Imrich, Ronald Ortner
https://arxiv.org/abs/2507.05821 https…

On cubic vertex-transitive graphs of given girth
A set of vertices of a graph is distinguishing if the only automorphism that preserves it is the identity. The minimal size of such sets, if they exist, is the distinguishing cost. The distinguishing costs of vertex transitive cubic graphs are well known if they are 1-arc-transitive, or if they have two edge orbits and either have girth 3 or vertex-stabilizers of order 1 or 2. There are many results about vertex-transitive cubic graphs of girth 4 with two edge orbits, but for larger girth alm…

Finite 2-groups having a cyclic or dihedral maximal subgroup and arc-transitive maps
Peice Hua
https://arxiv.org/abs/2508.05981 https://arxiv.org/pdf/2508.…

Finite 2-groups having a cyclic or dihedral maximal subgroup and arc-transitive maps
We classify all finite 2-groups that have a cyclic or dihedral maximal subgroup and determine their automorphism groups. Based on this result, we classify all pairs $ (G,\mathcal{M}) $, such that $ G $ is a finite 2-group and $ \mathcal{M} $ is a $ G $-arc-transitive map with Euler characteristic not being divisible by 4.

Translation Groups for arbitrary Gauge Fields in Synthetic Crystals with real hopping amplitudes
Marco Marciani
https://arxiv.org/abs/2508.08461 https://ar…

Translation Groups for arbitrary Gauge Fields in Synthetic Crystals with real hopping amplitudes
The Cayley-crystals introduced in [F. R. Lux and E. Prodan, Annales Henri Poincaré 25(8), 3563 (2024)] are a class of synthetic lattices whose Hamiltonians are symmetric under the simply transitive action of a generic discrete group G. We show that these systems naturally realize the generalization of the so-called magnetic translation groups to arbitrary discrete gauge groups. The one-body dynamics mimics that of a particle carrying multiple charges, each experiencing a distinct static gauge-…

Existence of Richter-Peleg Representation for General Preferences
Leandro Gorno, Paulo Klinger Monteiro
https://arxiv.org/abs/2508.08980 https://arxiv.org/…

Existence of Richter-Peleg Representation for General Preferences
This paper provides a general characterization of preferences that admit a Richter-Peleg representation without imposing completeness or transitivity. We establish that a binary relation on a nonempty set admits a Richter-Peleg representation if and only if it is "strongly acyclic" and its transitive closure is "separable". Strong acyclicity rules out problematic cycles among indifference classes, while separability limits the structural complexity of the relation. Our main result has two signi…

On tetravalent half-arc-transitive graphs
Jin-Xin Zhou
https://arxiv.org/abs/2508.21336 https://arxiv.org/pdf/2508.21336

On tetravalent half-arc-transitive graphs
Vertex-stabilizers of trivalent edge-transitive graphs have been classified by Tutte, Goldschmidt and some others in several previous papers. Tetravalent half-arc-transitive graphs form an important class of tetravalent edge-transitive graphs. Marušič and Nedela (2001) initiated the study of the problem of classifying vertex-stabilizers of tetravalent half-arc-transitive graphs, which has received extensive attention and considerable effort in the literature. In this paper, we solve this prob…

Markoff triples and generating pairs of $\mathrm{SL}_2(\mathbb{F}_p)$
Jo\~ao Campos-Vargas
https://arxiv.org/abs/2508.21671 https://arxiv.org/pdf/2508.2167…

Markoff triples and generating pairs of $\mathrm{SL}_2(\mathbb{F}_p)$
Consider the level sets of the Markoff equation $$\mathrm{M}_k: x^2 + y^2 + z^2 - xyz - 2 = k.$$ The phenomenon of strong approximation, as named by Bourgain, Gamburd, and Sarnak, predicts that every solution of $\mathrm{M}_k$ over $\mathbb{F}_p$ descends from a solution over $\mathbb{Z}$. Moreover, we expect that the action of Vieta involutions (taking $(x, y, z)$ to $(yz-x, y, z)$, $(x, xz-y, z)$, and $(x, y, xy-z)$) on $\mathrm{M}_k(\mathbb{F}_p)$ is essentially transitive. In terms of matri…

Replaced article(s) found for physics.soc-ph. https://arxiv.org/list/physics.soc-ph/new
[1/1]:
- Interdisciplinarity Revealed by Transitive Reduction of Citation Networks
H. AlMuhanna, V. Vasiliauskaite, T. S. Evans

PyPitfall: Dependency Chaos and Software Supply Chain Vulnerabilities in Python
Jacob Mahon, Chenxi Hou, Zhihao Yao
https://arxiv.org/abs/2507.18075 https://

PyPitfall: Dependency Chaos and Software Supply Chain Vulnerabilities in Python
Python software development heavily relies on third-party packages. Direct and transitive dependencies create a labyrinth of software supply chains. While it is convenient to reuse code, vulnerabilities within these dependency chains can propagate through dependencies, potentially affecting down-stream packages and applications. PyPI, the official Python package repository, hosts many packages and lacks a comprehensive analysis of the prevalence of vulnerable dependencies. This paper introduces…

A guide to constructing free transitive actions on median spaces
P\'en\'elope Azuelos
https://arxiv.org/abs/2507.22230 https://arxiv.org/pdf/2507.2…

A guide to constructing free transitive actions on median spaces
We construct large families of groups admitting free transitive actions on median spaces. In particular, we construct groups which act freely and transitively on the complete universal real tree with continuum valence such that any subgroup of the additive reals is realised as the stabiliser of an axis. We prove a more precise version of this, which implies that there are $2^{2^{\aleph_0}}$ pairwise non-isomorphic groups which admit a free transitive action on this real tree. We also construct …

On the Induced Neighbourhood of Vertex-Transitive Graphs
Aditya Joshi
https://arxiv.org/abs/2509.06030 https://arxiv.org/pdf/2509.06030

On the Induced Neighbourhood of Vertex-Transitive Graphs
We present new conditions that eliminate a large class of graphs from being induced neighbourhoods of finite vertex-transitive graphs.

Exponential decay for the random connection model using asymptotic transitivity
Frankie Higgs
https://arxiv.org/abs/2509.02310 https://arxiv.org/pdf/2509.0…

Exponential decay for the random connection model using asymptotic transitivity
We prove that the probability the cluster of the origin in a subcritical Poisson random connection model (RCM) has size at least $n$ decays exponentially as $n$ increases, under minimal assumptions. We extend a recent method of Vanneuville (arXiv:2304.12110) from Bernoulli percolation on vertex-transitive graphs to the RCM. The key idea is that the subcritical RCM can be constructed by site percolation on a very high-intensity RCM. The latter RCM becomes ``almost vertex-transitive'' in a cert…

Regular Model Checking for Systems with Effectively Regular Reachability Relation
Javier Esparza, Valentin Krasotin
https://arxiv.org/abs/2506.18833 https:…

Regular Model Checking for Systems with Effectively Regular Reachability Relation
Regular model checking is a well-established technique for the verification of regular transition systems (RTS): transition systems whose initial configurations and transition relation can be effectively encoded as regular languages. In 2008, To and Libkin studied RTSs in which the reachability relation (the reflexive and transitive closure of the transition relation) is also effectively regular, and showed that the recurrent reachability problem (whether a regular set $L$ of configurations is …

Transitivity of mutation of $\tau$-exceptional sequences in the $\tau$-tilting finite case
Aslak B. Buan, Eric J. Hanson, Bethany R. Marsh
https://arxiv.org/abs/2506.21372

Transitivity of mutation of $τ$-exceptional sequences in the $τ$-tilting finite case
We prove that mutation of complete $τ$-exceptional sequences is transitive for $τ$-tilting finite algebras.

Block-transitive t-(k^2,k,\lambda) designs associated to two dimensional projective special linear groups
Guoqiang Xiong, Haiyan Guan
https://arxiv.org/abs/2508.19515 https://…

Block-transitive t-(k^2,k,λ) designs associated to two dimensional projective special linear groups
This paper investigates block-transitive automorphism groups of t-(k^2,k,λ) designs. Let D be a non-trivial t-(k^2,k,λ) design, G \leq \Aut(D) be block-transitive with X\unlhd G\leq \Aut(X), where X = PSL(2,q)(q\geq4). Then q = 8 and D is a 2-(36,6,λ) design with λ\in \{2,6,9,12,18,36\}.

Cubic vertex-transitive graphs of girth seven
Maru\v{s}a Lek\v{s}e, Micael Toledo
https://arxiv.org/abs/2508.19880 https://arxiv.org/pdf/2508.19880

Cubic vertex-transitive graphs of girth seven
In this paper we classify cubic vertex-transitive graphs of girth $7$, based on their signature. Such a graph is either a truncation of an arc-transitive dihedral scheme on a $7$-regular graph, the skeleton of a rotary map of type $\{7,3\}$, a member of an infinite family of Cayley graphs, or is one of the of the generalised Petersen graphs $\text{Pet}(13,5)$, $\text{Pet}(15,4)$, $\text{Pet}(17,4)$ or the Coxeter graph. We show that for a cubic vertex-transitive graphs $Γ$ of girth $7$, if eve…

The set-theoretic Kaufmann-Clote question
Zachiri McKenzie
https://arxiv.org/abs/2507.01176 https://arxiv.org/pdf/2507.01176

The set-theoretic Kaufmann-Clote question
Let $\mathsf{M}$ be the set theory obtained from $\mathsf{ZF}$ by removing the collection scheme, restricting separation to $Δ_0$-formulae and adding an axiom asserting that every set is contained in a transitive set. Let $Π_n\textsf{-Collection}$ denote the restriction of the collection scheme to $Π_n$-formulae. In this paper we prove that for $n \geq 1$, if $\mathcal{M}$ is a model of $\mathsf{M}+Π_n\textsf{-Collection}+\mathsf{V=L}$ and $\mathcal{N}$ is a $Σ_{n+1}$-elementary end extens…

On the base size and minimal degree of transitive groups
Lorenzo Guerra, Attila Mar\'oti, Fabio Mastrogiacomo, Pablo Spiga
https://arxiv.org/abs/2506.17668

On the base size and minimal degree of transitive groups
Let $G$ be a permutation group, and denote with $μ(G)$ and $b(G)$ its minimal degree and base size respectively. We show that for every $\varepsilon>0$, there exists a transitive permutation group $G$ of degree $n$ with \[ μ(G)b(G) \geq n^{2-\varepsilon}. \] We also identify some classes of transitive and intransitive groups whose base size and minimal degree have a smaller upper bound, shared with primitive groups.

Vertex-transitive nut graph order-degree existence problem
Ivan Damnjanovi\'c
https://arxiv.org/abs/2507.02481 https://arxiv.org/…

Vertex-transitive nut graph order-degree existence problem
A nut graph is a nontrivial simple graph whose adjacency matrix has a simple eigenvalue zero such that the corresponding eigenvector has no zero entries. It is known that the order $n$ and degree $d$ of a vertex-transitive nut graph satisfy $4 \mid d$, $d \ge 4$, $2 \mid n$ and $n \ge d + 4$; or $d \equiv 2 \pmod 4$, $d \ge 6$, $4 \mid n$ and $n \ge d + 6$. Here, we prove that for each such $n$ and $d$, there exists a $d$-regular Cayley nut graph of order $n$. As a direct consequence, we obtain…

Model-theoretic Forcing in Transition Algebra
Go Hashimoto, Daniel G\u{a}in\u{a}
https://arxiv.org/abs/2506.22828 https://arxiv.org/p…

Model-theoretic Forcing in Transition Algebra
We study Löwenheim-Skolem and Omitting Types theorems in Transition Algebra, a logical system obtained by enhancing many sorted first-order logic with features from dynamic logic. The sentences we consider include compositions, unions, and transitive closures of transition relations, which are treated similarly to actions in dynamic logics to define necessity and possibility operators. We show that Upward Löwenheim-Skolem theorem, any form of compactness, and joint Robinson consistency proper…

The recurrence spectrum for dynamical systems beyond specification
Hiroki Takahasi
https://arxiv.org/abs/2509.01485 https://arxiv.org/pdf/2509.01485…

The recurrence spectrum for dynamical systems beyond specification
We introduce {\it (W')-specification} in terms of language decompositions of subshifts, and show that any recurrence set of a subshift with this property has full Hausdorff dimension. Our main result applies to a wide class of subshifts without specification, such as all $S$-gap shifts, some coded shifts, and the coding space of any transitive piecewise monotonic interval map with positive entropy. Further, for a wide class of piecewise expanding interval maps we show that any recurrence set ha…

Hamilton Cycles In Vertex-Transitive Graphs of Order 10p
Huye Chen, Jingjian Li, Hao Yu
https://arxiv.org/abs/2506.19888 https://arxi…

Hamilton Cycles In Vertex-Transitive Graphs of Order 10p
After a long term efforts, the Hamiltonian problem of connected vertex-transitive graphs of order $pq$ (where $p$ and $q$ are primes) was finally finshed in 2021, see [10]. Fifteen years ago, mathematicians began to challenge this problem for graphs of order $2pq$. Among of them, it was proved in 2012 (see [21]) that every connected vertex-transitive graph of order $10p$ (where $p\neq7$ is a prime) contains a Hamilton path, with the exception of a family of graphs which was recently confirmed i…

Perturbed infinite-state Markov systems with holes and its application
Haruyoshi Tanaka
https://arxiv.org/abs/2506.20053 https://arxi…

Perturbed infinite-state Markov systems with holes and its application
We consider a perturbed system $(X,φ(ε,\cdot))$, where $X$ is a topological Markov shift with a countably infinite state space, and $φ(ε,\cdot)$ is a real-valued potential on X depending on a small parameter $ε\in (0,1)$. We assume that for each $ε>0$, the system has a unique transitive component and a unique Gibbs measure (or more generally, a Ruelle-Perron-Frobenius (RPF) measure) $μ_ε$, while the unperturbed system possesses multiple transitive components and Gibbs measures on these …

Transformations of Triads and Seventh Chords: Group Extensions and Duality
Thomas M. Fiore, Thomas Noll, Ethan Bonnell, Hayden Pyle, No\'e Rodriguez, Meredith Williams, Sonia Cannas, Moreno Andreatta
https://arxiv.org/abs/2507.20811

Transformations of Triads and Seventh Chords: Group Extensions and Duality
Transformational music theory, pioneered by David Lewin, uses simply transitive group actions to analyze music. In this paper, we construct a simply transitive group action on a disjoint union of two sets, built from a simply transitive action on each set and an equivariant bijection connecting them. Motivational examples are the omnibus progression and the reflected omnibus progression, which involve the consonant triads and the dominant/half-diminished seventh chords, connected by the inclusi…

Block-transitive t-(k^2,k,\lam) designs and simple exceptional groups of Lie type
Xingyu Chen, Haiyan Guan
https://arxiv.org/abs/2508.18660 https://arxiv.o…

Block-transitive t-(k^2,k,\lam) designs and simple exceptional groups of Lie type
Let G be an automorphism group of a nontrivial t-(k^2,k,λ) design. In this paper, we prove that if G is block-transitive, then the socle of G cannot be a finite simple exceptional group of Lie type.

Classification of flag-transitive $2$-$(v, k, \lambda)$ designs with alternating group $A_n$($n \le 10$) as socle
Delu Tian, Qianfen Liao, Zhilin Zhang
https://arxiv.org/abs/2508.20716

Classification of flag-transitive $2$-$(v, k, λ)$ designs with alternating group $A_n$($n \le 10$) as socle
This paper is devoted to the classification of all flag-transitive point-primitive non-trivial $2$-$(v, k, λ)$ designs with the alternating group $A_n$($n \le 10$) as the socle of their automorphism groups, and 87 different designs are obtained up to isomorphism. The results of this study further improve the classification theory of designs under the action of almost simple groups, and provide reference for the follow-up study of similar problems.

Mass Functions and Asymptotic Behavior of Caloric Functions on Affine Buildings
Effie Papageorgiou, Bartosz Trojan
https://arxiv.org/abs/2506.17042 https:/…

Mass Functions and Asymptotic Behavior of Caloric Functions on Affine Buildings
We study the large-time asymptotic behavior of solutions to the discrete-time heat equation, i.e., caloric functions, on affine buildings, including those without transitive group actions. For each $p \in [1, \infty]$, we introduce a notion of a $p$-mass function and prove that caloric functions with initial data belonging to certain weighted-$\ell^1$ spaces or to the radial $\ell^1$ class, asymptotically decouple as the product of this mass function and the heat kernel. These results extend cl…

Intersections of longest cycles in vertex-transitive and highly connected graphs
Jie Ma, Ziyuan Zhao
https://arxiv.org/abs/2508.17438 https://arxiv.org/pdf…

Intersections of longest cycles in vertex-transitive and highly connected graphs
Motivated by the classical conjectures of Lovász, Thomassen, and Smith, recent work has renewed interest in the study of longest cycles in important graph families, such as vertex-transitive and highly connected graphs. In particular, Groenland et al.\ proved that if two longest cycles and in a graph share $m$ vertices, then there exists a vertex cut of size $O(m^{8/5})$ separating them, yielding improved bounds toward these conjectures. Their proof combines Turán-type arguments with computer…

Ornamentation lattices and intreeval hypergraphic lattices
Antoine Abram, Jose Bastidas, F\'elix G\'elinas, Vincent Pilaud, Andrew Sack
https://arxiv.org/abs/2508.01606 …

Ornamentation lattices and intreeval hypergraphic lattices
Given a directed graph $D$ with transitive closure $\operatorname{tc}(D)$ and path hypergraph $\mathbb{P}(D)$, we study the connections between the (acyclic) reorientation poset of $\operatorname{tc}(D)$, the (acyclic) sourcing poset of $\mathbb{P}(D)$, and the (acyclic) ornamentation poset of $D$. Geometrically, the acyclic reorientation poset of $\operatorname{tc}(D)$ (resp. the acyclic sourcing poset of $\mathbb{P}(D)$) is the transitive closure of the skeleton of the graphical zonotope of $…

Automorphism groups of measures on the Cantor space. Part II: Abstract homogeneous measures
Piotr Niemiec
https://arxiv.org/abs/2506.20797 https://

Automorphism groups of measures on the Cantor space. Part II: Abstract homogeneous measures
The main aim of the paper is to introduce a new class of (semigroup-valued) measures that are ultrahomogeneous on the Boolean algebra of all clopen subsets of the Cantor space and to study their automorphism groups. A characterisation, in terms of the so-called trinary spectrum of a measure, of ultrahomogeneous measures such that the action of their automorphism groups is (topologically) transitive or minimal is given. Also sufficient and necessary conditions for the existence of a dense (or co…

Separating subsets from their images
Marco Barbieri, Maru\v{s}a Lek\v{s}e, Primo\v{z} Poto\v{c}nik, Kamilla Rekv\'enyi
https://arxiv.org/abs/2508.20731 https://

Separating subsets from their images
Let $G$ be a transitive permutation group. In this paper, we introduce and study the parameter $\m(G)$, which estimates the size of the largest set of points $A$ such that there exists a permutation $g$ with the property that $A \cap A^g$ is empty. In particular, we focus on deriving general bounds for arbitrary transitive groups, and on the asymptotic behaviour of certain families of primitive groups.

Minor-excluded graphs and soficity
Oriol Sol\'e-Pi
https://arxiv.org/abs/2508.06731 https://arxiv.org/pdf/2508.06731

Minor-excluded graphs and soficity
A random rooted graph is said to be sofic if it is the Benjamini-Schramm limit of a sequence of finite graphs. Given any finite graph $H$, we prove that every one-ended, unimodular random rooted graph that does not have H as a minor must be sofic. The hypothesis regarding the number of ends can be dropped under the additional assumption that the graph is quasi-transitive.

CR tournaments
Jing Zeng, Lihua You, Xinghui Zhao
https://arxiv.org/abs/2508.07332 https://arxiv.org/pdf/2508.07332…

CR tournaments
The determinant of a tournament $T$ is defined as the determinant of the skew-adjacency matrix of $T$. For a positive odd integer $k$, let $\mathcal{D}_k$ be the set of tournaments whose all subtournaments have determinant at most $k^2$. Some existing results show that, for $k \in \{1,3,5\}$, a tournament $T \in \mathcal{D}_k \backslash \mathcal{D}_{k-2}$ ($T \in \mathcal{D}_1$ when $k=1$) if and only if $T$ is switching equivalent to a transitive blowup of $L_{k+1}$, where $L_{k+1}$ is a tourn…

Measures of Systems of Oscillators and Properties of Trajectories
Vsevolod Sakbaev (Steklov Mathematical Institute of Russian Academy of Sciences), Igor Volovich (Steklov Mathematical Institute of Russian Academy of Sciences)
https://arxiv.org/abs/2506.18093

Measures of Systems of Oscillators and Properties of Trajectories
Properties of trajectories of systems of harmonic oscillators equipped with a point, absolutely continuous or singular measure are considered in this paper. Linear flow of an infinite system of oscillators on an infinite dimensional tori in the phase space are studied. It was shown in [28] that for infinite-dimensional linear flows of a countable system of oscillators there is a new type of trajectories that is not periodic and has no transitive projection on any 4-dimensional symplectic subspa…

The gonality of circulant graphs
Lisa Cenek, Lizzie Ferguson, Eyobel Gebre, Cassandra Marcussen, Jason Meintjes, Ralph Morrison, Liz Ostermeyer, Shefali Ramakrishna
https://arxiv.org/abs/2508.05761

The gonality of circulant graphs
The gonality of a graph measures how difficult it is to move chips around the entirety of a graph according to certain chip-firing rules without introducing debt. In this paper we study the gonality of circulant graphs, a class of vertex-transitive graphs that can be specified by their number of vertices together with a list of cyclic adjacency relations satisfied by all vertices. We provide a universal upper bound on the gonality of all circulant graphs with a fixed adjacency list, which holds…

An Algorithm for Computing Hopf--Galois Structures and Skew Bracoids of Low Degree
Andrew Darlington
https://arxiv.org/abs/2508.03372 https://arxiv.org/pdf…

An Algorithm for Computing Hopf--Galois Structures and Skew Bracoids of Low Degree
Making use of the fact that Hopf-Galois structures on separable extensions and skew bracoids are both intrinsically connected to transitive subgroups of the holomorph, we present an algorithm to classify and enumerate these objects in several low degree cases. Our approach allows us to greatly extend existing computational results for Hopf-Galois structures, while building on the existing algorithms presented in this area.

Symmetry classes of Hamiltonian cycles
Julia Baligacs (TU Darmstadt), Sofia Brenner (Universit\"at Kassel), Annette Lutz (TU Darmstadt), Lena Volk (TU Darmstadt)
https://arxiv.org/abs/2506.21337

Symmetry classes of Hamiltonian cycles
We initiate the study of Hamiltonian cycles up to symmetries of the underlying graph. Our focus lies on the extremal case of Hamiltonian-transitive graphs, i.e., Hamiltonian graphs where, for every pair of Hamiltonian cycles, there is a graph automorphism mapping one cycle to the other. This generalizes the extensively studied uniquely Hamiltonian graphs. In this paper, we show that Cayley graphs of abelian groups are not Hamiltonian-transitive (under some mild conditions and some non-surprisin…

Dynamics of Enveloping Semigroup of Flows
Sushmita Yadav, Puneet Sharma
https://arxiv.org/abs/2507.16232 https://arxiv.org/pdf/2507.1…

Dynamics of Enveloping Semigroup of Flows
In this article, we relate the dynamics of a flow $(X, T)$ with the dynamics of the induced flow $(E(X), T)$ where $E(X)$ is the enveloping semigroup of flow $(X, T)$. We establish that a flow $(X, T)$ is distal if and only if the induced flow is also distal. We prove that while the induced flow on the enveloping semigroup of an equicontinuous flow is equicontinuous, the converse holds when $(X, T)$ is point transitive. We prove that for any flow $(X,T)$, $(E(X),T)$ is isomorphic to $(E(E(X)),T…

Irreducible finite-index representations of automorphism groups of trees
Federico Viola
https://arxiv.org/abs/2508.02367 https://arxiv.org/pdf/2508.02367…

Irreducible finite-index representations of automorphism groups of trees
We consider a locally finite tree T where every vertex has degree >= 3, and a closed noncompact subgroup G of the automorphism group Aut(T), with Tits' independence property (P) and with transitive action on the boundary of the tree. We show that G does not have continuous irreducible representations to a locally convex topological vector space over R, C or H that preserve a continuous nondegenerate sesquilinear form of index p > 1. As the representations of index 1 are already classified, this…

Binomiality of colored Gaussian models
Benjamin Biaggi, Jan Draisma, Magdal\'ena Mi\v{s}inov\'a
https://arxiv.org/abs/2507.06437 https://

Binomiality of colored Gaussian models
Following earlier work by Coons-Maraj-Misra-Sorea and Misra-Sullivant, we study colored, undirected Gaussian graphical models, and present a necessary and sufficient condition for such a model to have binomial vanishing ideal. These conditions involve Jordan schemes, a variant of association schemes, well-known structures in algebraic combinatorics. Using association schemes without transitive group action, we refute the conjecture by Coons-Maraj-Misra-Sorea that binomiality implies that the co…

A directed Andr\'asfai-Erd\H{o}s-S\'os theorem and chromatic profiles of oriented cycles
Yisai Xue
https://arxiv.org/abs/2509.07760 https://arxiv.o…

A directed Andrásfai-Erdős-Sós theorem and chromatic profiles of oriented cycles
The chromatic profile of a digraph $H$, denoted by $δ_χ^{+}(H,k)$, is the infimum $d$ such that any $H$-free digraph $D$ on $n$ vertices with minimum out-degree $δ^{+}(D) \ge dn$ must be $k$-colorable. We determine the exact chromatic profile for several fundamental classes of digraphs. Our main result is a directed analogue of the Andrásfai-Erdős-Sós theorem, stating that $δ_χ^{+}(T_r, r-1)=\frac{3 r-7}{3 r-4}$, where $T_r$ is the transitive tournament on $r$ vertices. We then determin…

Some calculations of centralizer rings of a complex reflection group
Masashi Kosuda, Manabu Oura, Sarbaini
https://arxiv.org/abs/2507.20521 https://arxiv.…

Some calculations of centralizer rings of a complex reflection group
Let H1 be the complex reflection group of order 96. For the tensor products of faithful transitive permutation representations of H1, we determine the structures of the centralizer rings. This complements the work of Imamura-Kosuda-Oura.

Roux schemes which carry association schemes locally
Alexander L. Gavrilyuk, Jesse Lansdown, Akihiro Munemasa, Sho Suda
https://arxiv.org/abs/2507.18960 https://

Roux schemes which carry association schemes locally
A roux scheme is an association scheme formed from a special "roux" matrix and the regular permutation representation of an associated group. They were introduced by Iverson and Mixon for their connection to equiangular tight frames and doubly transitive lines. We show how roux matrices can be produced from association schemes and characterise roux schemes for which the neighbourhood of a vertex induces an association scheme possessing the same number of relations as the thin radical. An import…

Conformal Rigidity and Spectral Embeddings of Graphs
Jo\~ao Gouveia, Stefan Steinerberger, Rekha R. Thomas
https://arxiv.org/abs/2506.20541 https://…

Conformal Rigidity and Spectral Embeddings of Graphs
We investigate the structure of conformally rigid graphs. Graphs are conformally rigid if introducing edge weights cannot increase (decrease) the second (last) eigenvalue of the Graph Laplacian. Edge-transitive graphs and distance-regular graphs are known to be conformally rigid. We establish new results using the connection between conformal rigidity and edge-isometric spectral embeddings of the graph. All $1$-walk regular graphs are conformally rigid, a consequence of a stronger property of t…

Source characterization of the hypergraphic posets
F\'elix G\'elinas
https://arxiv.org/abs/2508.16006 https://arxiv.org/pdf/2508.16006

Source characterization of the hypergraphic posets
For a hypergraph $\mathbb{H}$ on $[n]$, the hypergraphic poset $P_\mathbb{H}$ is the transitive closure of the oriented $1$-skeleton of the hypergraphic polytope $Δ_\mathbb{H}$. In a recent paper, N. Bergeron and V. Pilaud provided a characterization of $P_\mathbb{H}$ based on the sources of acyclic orientations for interval hypergraphs. The goal of this work is to extend this source characterization of $P_\mathbb{H}$ for arbitrary hypergraphs on $[n]$.

On nut graphs with two vertex and three edge orbits
Ksenija Rozman, Primo\v{z} \v{S}parl
https://arxiv.org/abs/2508.17842 https://arxiv.org/pdf/2508.17842

On nut graphs with two vertex and three edge orbits
Nut graphs are graphs whose adjacency matrix is singular with one-dimensional null space spanned by a vector with no zero entries. In a recent paper, Bašić, Fowler and Pisanski proved that the automorphism group of a nut graph has more orbits on the edge set than on the vertex set. They classified all orders for which a vertex-transitive nut graph with precisely two edge orbits exists, and conjectured that a nut graph with two vertex and three edge orbits exists for each non-prime order $n \g…

Maximal transitivity of the cactus group on standard Young tableaux
Sophia Liao, Leonid Rybnikov
https://arxiv.org/abs/2506.16561 https://

Maximal transitivity of the cactus group on standard Young tableaux
The action of the cactus group $C_n$ on Young tableaux of a given shape $λ$ goes back to Berenstein and Kirillov and arises naturally in the study of crystal bases and quantum integrable systems. We show that this action is $2$-transitive on standard Young tableaux of the shape $λ$ if and only if $λ$ is not self-transpose and not a single hook. Moreover, we show that in these cases, the image of the cactus group in the permutation group of standard Young tableaux is either the whole permutat…