Tootfinder

A coalition of collegiate and professional press freedom groups urges campus administrators to respect the rights of student journalists covering protests (College Media Association)
https://collegemedia.org/release-colle

RELEASE: Collegiate Media Associations, Supporters Urge Campus Administrators to Support Student Journalists - College Media Association
College Media Association, Associated Collegiate Press, Society of Professional Journalists, Student Press Law Center and Foundation for Individual Rights and Expression have joined together to urge campus administrators to be supportive of student journalists covering current events.

Generalized Cayley graphs of complete groups
Qianfen Liao, Liu Weijun
https://arxiv.org/abs/2405.00297 https://arxiv.org/pdf/2405.002…

Generalized Cayley graphs of complete groups
A group $G$ is complete group if it satisfies $Z(G) = e$ and Aut$(G)$ = Inn$(G)$. In this paper, we study the basic properties of generalized Cayley graphs and characterize several classes of isomorphic generalized Cayley graphs of complete group. As an application, we complete the classification of restricted GCI-groups for symmetric groups.

Galaxy groups and clusters and their brightest #galaxies within the cosmic web: https://www.aanda.org/articles/aa/full_html/2024/01/aa47504-23/aa47504-23.html -> Galaxy groups and clusters do not differ just in the number of galaxies: https://www.eurekalert.org/news-releases/1035766

This https://arxiv.org/abs/2007.10694 has been replaced.
link: https://scholar.google.com/scholar?q=a

Rationality of representation zeta functions of compact $p$-adic analytic groups
We prove that for any FAb compact $p$-adic analytic group $G$, its representation zeta function is a finite sum of terms $n_{i}^{-s}f_{i}(p^{-s})$, where $n_{i}$ are natural numbers and $f_{i}(t)\in\mathbb{Q}(t)$ are rational functions. Meromorphic continuation and rationality of the abscissa of the zeta function follow as corollaries. If $G$ is moreover a pro-$p$ group, we prove that its representation zeta function is rational in $p^{-s}$. These results were proved by Jaikin-Zapirain for $p>2…

Cayley graphs and G-graphs of Gyro-groups
Neda Moradi, Gholam Hossein Fath-Tabara, Alain Bretto
https://arxiv.org/abs/2404.19741 https://

Cayley graphs and G-graphs of Gyro-groups
In this paper the structure of the Cayley graphs and G-graphs of some gyro-groups are studied and some properties of them will be proved. Moreover we review some special gyro-groups including: gyro-commutative gyrogroups, dihedral gyro-groups and dihedralized gyro-groups. Then we try to establish some important properties of their associated G-graphs. Finally we will examine the symmetry of Cayley graphs and G-graphs of some gyro-groups.

On the Schwartz estimate for Hodge Laplacians on semisimple Lie groups
Zhicheng Han
https://arxiv.org/abs/2404.19091 https://arxiv.or…

On the Schwartz estimate for Hodge Laplacians on semisimple Lie groups
In this paper, we prove Schwartz estimates for Hodge Laplacian and Dirac operators on semisimple Lie groups. Alongside, we gives a version of Kuga lemma for its Lie algebra cohomology. This is a generalization of similar results on symmetric spaces. The main purpose of such estimates is to study the heat problem not only in the scalar case, but also for sections of vector bundles on homogeneous spaces using Fourier analysis.

This https://arxiv.org/abs/2401.16081 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On some topological equivalences for moduli spaces of $G$-bundles
Let $X$ be a smooth projective curve of genus $g \geq 3$, and let $G$ be a nontrivial connected reductive affine algebraic group over $\mathbb{C}$. Examining the moduli spaces of regularly stable $G$-Higgs bundles and holomorphic $G$-connections with a fixed topological type $d\in π_1(G)$ over $X$, we establish that the $k$-th homotopy groups of these two moduli spaces are isomorphic for $k \leq 2g-4$. We also prove that the mixed Hodge structures on the rational cohomology groups of these two…

spring/summer #running season in #nyc has returned: sidewalks full to the curb with groups walking 4-5 across, bike lanes filled with mopeds & motorcycles.

Dynamical Systems on Compact Metrizable Groups
Binghui Xiao
https://arxiv.org/abs/2402.19074 https://arxiv.org/pdf/2402.19074<…

Dynamical Systems on Compact Metrizable Groups
This paper mainly studies the theory of dynamical systems on compact metrizable groups, with a special focus on extending the maximal entropy theorem and the ergodicity of invariant measure convolution from the isomorphic case to the surjective homomorphism case. It explores in detail the dynamical systems under surjective homomorphisms, especially the variation of measure entropy. Let $G_{2}$ be a compact metric group acting freely on $G_{1}$, and the continuous mapping $T_{2}$ $G_{2}-$commute…

Iraq criminalises LGBTQ relationships in 'attack on human rights'
https://www.thepinknews.com/2024/04/29/iraq-human-rights/

Iraq’s criminalisation of same-sex relationships and LGBTQ+ people an ‘attack on human rights’
Iraq’s parliament have passed a law criminalising same-sex relationships and trans people, with human rights groups rejecting the decision.

Jewish Australians Are Rejecting the Zionist Establishment https://jacobin.com/2024/04/jewish-council-of-australia-zionism/

Jewish Australians Are Rejecting the Zionist Establishment
Inspired by anti-fascist organizing in the 1940s, a group of progressive Jewish activists have formed the Jewish Council of Australia. Its goal is to challenge the hegemony of right-wing, Zionist groups that claim to speak for all Jewish Australians.

This https://arxiv.org/abs/2007.10694 has been replaced.
link: https://scholar.google.com/scholar?q=a

Rationality of representation zeta functions of compact $p$-adic analytic groups
We prove that for any FAb compact $p$-adic analytic group $G$, its representation zeta function is a finite sum of terms $n_{i}^{-s}f_{i}(p^{-s})$, where $n_{i}$ are natural numbers and $f_{i}(t)\in\mathbb{Q}(t)$ are rational functions. Meromorphic continuation and rationality of the abscissa of the zeta function follow as corollaries. If $G$ is moreover a pro-$p$ group, we prove that its representation zeta function is rational in $p^{-s}$. These results were proved by Jaikin-Zapirain for $p>2…

Meta, Google, OpenAI, child safety group Thorn, nonprofit All Tech Is Human, and other AI groups sign on to an initiative to add new child safety measures (Deepa Seetharaman/Wall Street Journal)
https://www.wsj.com/tech/ai/ai-developers-

Hook-Lengths, Symplectic/Orthogonal Contents and Amdeberhan's Conjectures
Chenglang Yang
https://arxiv.org/abs/2404.01973 https://

Hook-Lengths, Symplectic/Orthogonal Contents and Amdeberhan's Conjectures
The symplectic/orthogonal contents of partitions are related to the dimensions of irreducible representations of symplectic/orthogonal groups. In 2012, motivated by Nekrasov-Okounkov's hook-length formula and Stanley's hook-content formula, Amdeberhan proposed several conjectures about infinite product formulas for certain generating functions of hook-lengths and symplectic/orthogonal contents. Some special cases of his conjectures were recently proved by Amdeberhan, Andrews and Ballantine. In …

This https://arxiv.org/abs/2404.08977 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

RoNID: New Intent Discovery with Generated-Reliable Labels and Cluster-friendly Representations
New Intent Discovery (NID) strives to identify known and reasonably deduce novel intent groups in the open-world scenario. But current methods face issues with inaccurate pseudo-labels and poor representation learning, creating a negative feedback loop that degrades overall model performance, including accuracy and the adjusted rand index. To address the aforementioned challenges, we propose a Robust New Intent Discovery (RoNID) framework optimized by an EM-style method, which focuses on constr…

Quantized semisimple Lie groups
Rita Fioresi, Robert Yuncken
https://arxiv.org/abs/2403.17180 https://arxiv.org/pdf/2403.17180…

Quantized semisimple Lie groups
These notes present a quick introduction to the q-deformations of semisimple Lie groups from the point of view of unitary representation theory. In order to remain concrete, we concentrate entirely on the case of the lie algebra $\mathrm{sl}(2,\mathbb{C})$ and its associated compact and complex semisimple Lie groups $\mathrm{SU}(2)$ and $\mathrm{SL}(2,\mathbb{C})$. We treat the following topics: The quantized enveloping algebra and its representations; Hopf algebras and the various notions of…

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.

Huge funding 💰from influential conservative donor networks is flowing into groups affiliated with a conservative venture aimed at creating a Republican "government-in-waiting," including over💥 $55 million from groups linked to conservative activist #Leonard #Leo and the

Leonard Leo, Koch networks pour millions into prep for potential second Trump administration
Huge funding from influential conservative donor networks is flowing into a conservative venture aimed at creating a Republican "government-in-waiting."

My latest CSO column examines the lack of easy solutions to the ransomware problem despite the recent high-profile takedowns of top ransomware groups.
Many thanks to Bob Kolasky of Exiger, @…, @… and Adam Meyers of CrowdStrike for their insights.
https://www.csoonline.com/article/2067614/no-easy-solutions-to-the-ransomware-threat-despite-takedowns.html

The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds
Isolda Cardoso, Ana Cosgaya, Silvio Reggiani
https://arxiv.org/abs/2404.19177

The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds
A real Lie algebra is said to be characteristically solvable if its derivation algebra is solvable. We explicitly determine the moduli space of left-invariant metrics, up to isometric automorphism, for $6$-dimensional nilmanifolds whose associated Lie algebra is characteristically solvable. We also compute the corresponding full isometry groups. For each left-invariant metric on these nilmanifolds we compute the index and distribution of symmetry. In particular, we find the first known examples…

Poissonian Actions of Polish Groups
Nachi Avraham-Re'em, Emmanuel Roy
https://arxiv.org/abs/2403.19567 https://arxiv.org/pdf/2403…

Poissonian Actions of Polish Groups
We define and study Poissonian actions of Polish groups as a framework to Poisson suspensions, characterize them spectrally, and provide a complete characterization of their ergodicity. We further construct 'spatial' Poissonian actions, answering partially a question of Glasner, Tsirelson & Weiss about Lévy groups. We also construct for every diffeomorphism group an ergodic free spatial probability preserving actions. This constitutes a new class of Polish groups admitting non-essentially coun…

#Abortion Ban Extremists Are Using a Slave Law to Repress Women - OtherWords
https://otherwords.org/abortion-ban-extremists-are-using-a-slave-law…

Abortion Ban Extremists Are Using a Slave Law to Repress Women - OtherWords
Texas is trying to ban the use of its roads by people seeking care outside the state — and even dispatching right-wing vigilante groups to chase them.

Tenant protection bills sponsored by Maryland's leading yimby legislator Vaughn Stewart pass House of Delegates, while modest housing production bill introduced by Gov Moore moves slowly (and may get watered down) in the face of opposition from homeowner groups & local governments.

Landlord-tenant bills provide drama in 'Crossover Day' House action - Maryland Matters
Republican lawmaker longs for bill that seeks to punish 'slum-tenants.

This https://arxiv.org/abs/2210.17179 has been replaced.
link: https://scholar.google.com/scholar?q=a

Picard Groups of Some Quot Schemes
Let $C$ be a smooth projective curve over the field of complex numbers $\mathbb{C}$ of genus $g(C)>0$. Let $E$ be a locally free sheaf on $C$ of rank $r$ and degree $e$. Let $\mathcal{Q}:={\rm Quot}_{C/\mathbb{C}}(E,k,d)$ denote the Quot scheme of quotients of $E$ of rank $k$ and degree $d$. For $k>0$ and $d\gg 0$ we compute the Picard group of $\mathcal{Q}$.

Galois theory and homology in quasi-abelian functor categories
Nadja Egner
https://arxiv.org/abs/2403.12750 https://arxiv.org/pdf/240…

Galois theory and homology in quasi-abelian functor categories
Given a finite category T, we consider the functor category [T,A], where A can in particular be any quasi-abelian category. Examples of quasi-abelian categories are given by any abelian category but also by non-exact additive categories as the categories of torsion(-free) abelian groups, topological abelian groups, locally compact abelian groups, Banach spaces and Fréchet spaces. In this situation, the categories of various internal categorical structures in A, such as the categories of intern…

This https://arxiv.org/abs/2401.01327 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The $r$-matrix structure of Hitchin systems via loop group uniformization
In this work, the description of the moduli space of principal $G$-bundles as double quotient of loop groups is used to construct an étale local $r$-matrix for the Hitchin integrable system.

Mackey formula for disconnected reductive groups
Sergio C\'ia (Sorbonne Universite)
https://arxiv.org/abs/2403.13407 https://arxi…

Mackey formula for disconnected reductive groups
We prove a Mackey formula for representations of finite groups of Lie type, in the case where the groups come from disconnected reductive groups.

Property owners: "Homelessness is out of control, do something!"
"Ok, here's a shelter and space for daytime showers, laundry, counseling and job training."
Property owners: "Not like that!"
https://www.sfchronicle.com/sf/artic…

This https://arxiv.org/abs/1103.5906 has been replaced.
link: https://scholar.google.com/scholar?q=a<…

Torsion groups of elliptic curves over quadratic fields
We describe methods to determine all the possible torsion groups of an elliptic curve that actually appear over a fixed quadratic field. We use these methods to find, for each group that can appear over a quadratic field, the field with the smallest absolute value of it's discriminant such that there exists an elliptic curve with that torsion. We also examine the interplay of the torsion and rank over a fixed quadratic field and see that what happens is very different than over $\Q$. Finally we…

This https://arxiv.org/abs/2402.13452 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSI_…

LocalTweets to LocalHealth: A Mental Health Surveillance Framework Based on Twitter Data
Prior research on Twitter (now X) data has provided positive evidence of its utility in developing supplementary health surveillance systems. In this study, we present a new framework to surveil public health, focusing on mental health (MH) outcomes. We hypothesize that locally posted tweets are indicative of local MH outcomes and collect tweets posted from 765 neighborhoods (census block groups) in the USA. We pair these tweets from each neighborhood with the corresponding MH outcome reported …

I keep meeting students who feel they *must* test their variables for normality before analysis.
I tell them there's no need, & if the test tells them it's normal it's only because N is too small.
I decided to run some simulations to check, though, whether e.g., t-tests degraded more for non-normal data & small Ns.
I was a bit surprised by the result: CI coverage degrades for normal vars just as badly as other symmetric dists, but skewed distributions…

Interesting overview by #NYT of Iranian proxies, it's not so simple as sometimes portrayed, lots of different groups with different levels of control by Iran. (giftlink)

How Iran Shapes the Mideast: Power by Proxy
A guide to the armed groups that let Iran extend its influence throughout the region.

That’s….one way to describe it…
AP: “On Super Bowl broadcast, ‘He Gets Us’ ads featuring Jesus stand out for change-of-pace message”
Then there’s the more accurate way to describe it...
USA Today: “Super Bowl Jesus Ad funded by groups fostering "hateful Christian Nationalism"

Poissonian Actions of Polish Groups
Nachi Avraham-Re'em, Emmanuel Roy
https://arxiv.org/abs/2403.19567 https://arxiv.org/pdf/2403…

Poissonian Actions of Polish Groups
We define and study Poissonian actions of Polish groups as a framework to Poisson suspensions, characterize them spectrally, and provide a complete characterization of their ergodicity. We further construct 'spatial' Poissonian actions, answering partially a question of Glasner, Tsirelson & Weiss about Lévy groups. We also construct for every diffeomorphism group an ergodic free spatial probability preserving actions. This constitutes a new class of Polish groups admitting non-essentially coun…

Hippocratic AI, which is building an LLM for health care, raised a $53M Series A co-led by Premji Invest and General Catalyst at a $500M valuation (Financial Times)
https://t.co/qat1g7ht24

Analysing 2-$(v,k,2)$ designs admitting a flag-transitive almost simple automorphism group with socle $PSL(2,q)$ by means of conics and hyperovals of $PG(2,q)$
Alessandro Montinaro, Yanwei Zhao, Zhilin Zhang, Shenglin Zhou
https://arxiv.org/abs/2404.19190

Analysing 2-$(v,k,2)$ designs admitting a flag-transitive almost simple automorphism group with socle $PSL(2,q)$ by means of conics and hyperovals of $PG(2,q)$
The classification of the $2$-designs with $λ=2$ admitting a flag-transitive automorphism groups with socle $PSL(2,q)$ is completed by settling the two open cases in \cite{ABDT}. The result is achieved by using conics and hyperovals of $PG(2,q)$.

On geodesic orbit nilmanifolds
Yu. G. Nikonorov
https://arxiv.org/abs/2402.17548 https://arxiv.org/pdf/2402.17548

On geodesic orbit nilmanifolds
The paper is devoted to the study of geodesic orbit Riemannian metrics on nilpotent Lie groups. The main result is the construction of continuous families of pairwise non-isomorphic connected and simply connected nilpotent Lie groups, every of which admits geodesic orbit metrics. The minimum dimension of groups in the constructed families is $10$.

This https://arxiv.org/abs/2305.04981 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

The Milky Way Bar Pattern Speed using Hercules and Gaia DR3
The distribution of moving groups in the solar neighborhood has been used to constrain dynamical properties of the Milky Way for decades. The kinematic bimodality between the main mode (Hyades, Pleiades, Coma Berenices, and Sirius) and Hercules can be explained by two different bar models -- via the outer Lindblad resonance of a bar with a high pattern speed ($\sim$55 km s$^{-1}$ kpc$^{-1}$), or via the corotation resonance of a bar with a low pattern speed ($\sim$40 km s$^{-1}$ kpc$^{-1}$). Re…

Tenant protection bills sponsored by Maryland's leading yimby legislator Vaughn Stewart pass House of Delegates, while modest housing production bill introduced by Gov Moore moves slowly (and may get watered down) in the face of opposition from homeowner groups & local governments.

Landlord-tenant bills provide drama in 'Crossover Day' House action - Maryland Matters
Republican lawmaker longs for bill that seeks to punish 'slum-tenants.

Galois theory and homology in quasi-abelian functor categories
Nadja Egner
https://arxiv.org/abs/2403.12750 https://arxiv.org/pdf/240…

Galois theory and homology in quasi-abelian functor categories
Given a finite category T, we consider the functor category [T,A], where A can in particular be any quasi-abelian category. Examples of quasi-abelian categories are given by any abelian category but also by non-exact additive categories as the categories of torsion(-free) abelian groups, topological abelian groups, locally compact abelian groups, Banach spaces and Fréchet spaces. In this situation, the categories of various internal categorical structures in A, such as the categories of intern…

This https://arxiv.org/abs/2306.02989 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finite-dimensional Nichols algebras of simple Yetter-Drinfeld modules (over groups) of prime dimension
Over fields of characteristic zero, we determine all absolutely irreducible Yetter-Drinfeld modules over groups that have prime dimension and yield a finite-dimensional Nichols algebra. To achieve our goal, we introduce orders of braided vector spaces and study their degenerations and specializations.

This https://arxiv.org/abs/2402.12793 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Harish-Chandra Theorem for Two-parameter Quantum Groups
The centre of two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ is determined through the Harish-Chandra homomorphism. Based on the Rosso form and the representation theory of weight modules, we prove that when rank $\mathfrak{g}$ is even, the Harish-Chandra homomorphism is an isomorphism, and the centre of the quantum group $\breve{U}_{r,s}(\mathfrak{g})$ of the weight lattice type is isomorphic to a polynomial algebra; and when rank $\mathfrak{g}$ is odd, we figure out a new generator of t…

Property owners: "Homelessness is out of control, do something!"
"Ok, here's a shelter and space for daytime showers, laundry, counseling and job training."
Property owners: "Not like that!"
https://www.sfchronicle.com/sf/artic…

"Tomorrow is Holocaust Memorial Day, an international day to remember the six million Jews murdered during the Holocaust, the millions of other people murdered under Nazi persecution of other groups and more recent genocides in Cambodia, Rwanda, Bosnia and now Gaza."
Kate Osamor, Labour MP suspended by the party bosses for making this factual statement.

Polymatroids are to finite groups as matroids are to finite fields
Ed Swartz, Prairie Wentworth-Nice, Alexander Xue
https://arxiv.org/abs/2402.17582 https:…

Polymatroids are to finite groups as matroids are to finite fields
Given a subgroup $\mathcal{H}$ of a product of finite groups $\mathcal{G} = \displaystyle\prod^n_{i=1} Γ_i$ and $b>1,$ we define a polymatroid $P(\mathcal{H},b).$ If all of the $Γ_i$ are isomorphic to $\mathbb{Z}/p\mathbb{Z},$ $p$ a prime, and $b=p,$ then $P(\mathcal{H},b)$ is the usual matroid associated to any $\mathbb{Z}/p\mathbb{Z}$-matrix whose row space equals $\mathcal{H}.$ In general, there are many ways in which the relationship between $P(\mathcal{H},b)$ and $\mathcal{H}$ mirrors th…

This https://arxiv.org/abs/2012.01324 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the Brauer groups of fibrations
Let $\mathcal{X}\rightarrow C$ be a dominant morphism between smooth irreducible varieties over a finitely generated field $k$ such that the generic fiber $X$ is smooth, projective and geometrically connected. Assuming that $C$ is a curve with function field $K$, we build a relation between the Tate-Shafarevich group for $\mathrm{Pic}^0_{X/K}$ and the geometric Brauer groups for $\mathcal{X}$ and $X$, generalizing a theorem of Artin and Grothendieck for fibered surfaces to arbitrary relative di…

👍 Civil Rights Groups Call For Baltimore's Francis Scott Key Bridge To Be Renamed Due To Namesake's Slavery Ties | Essence
https://www.essence.com/news/civil-rights-group-wants-francis-scott-key-bridge-renamed/

Civil Rights Groups Call For Baltimore’s Francis Scott Key Bridge To Be Renamed Due To Namesake’s Slavery Ties
Civil Rights groups are calling on the Maryland state government to rename the Francis Scott Key Bridge because Key was reportedly a slave owner.  The Caucus of African American Leaders, […]

This https://arxiv.org/abs/2312.15745 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finite almost simple groups whose holomorph contains a solvable regular subgroup
In our previous paper, we gave a complete list of the finite non-abelian simple groups whose holomorph contains a solvable regular subgroup. In this paper, we refine our previous work by considering all finite almost simple groups. In particular, our result yields a complete characterization of the finite almost simple groups which occur as the type of a Hopf-Galois structure on a solvable extension, or equivalently, the additive group of a skew brace having a solvable multiplicative group.

Polymatroids are to finite groups as matroids are to finite fields
Ed Swartz, Prairie Wentworth-Nice, Alexander Xue
https://arxiv.org/abs/2402.17582 https:…

Polymatroids are to finite groups as matroids are to finite fields
Given a subgroup $\mathcal{H}$ of a product of finite groups $\mathcal{G} = \displaystyle\prod^n_{i=1} Γ_i$ and $b>1,$ we define a polymatroid $P(\mathcal{H},b).$ If all of the $Γ_i$ are isomorphic to $\mathbb{Z}/p\mathbb{Z},$ $p$ a prime, and $b=p,$ then $P(\mathcal{H},b)$ is the usual matroid associated to any $\mathbb{Z}/p\mathbb{Z}$-matrix whose row space equals $\mathcal{H}.$ In general, there are many ways in which the relationship between $P(\mathcal{H},b)$ and $\mathcal{H}$ mirrors th…

This https://arxiv.org/abs/2402.00562 has been replaced.
link: https://scholar.google.com/scholar?q=a

Endomorphisms of Linear Block Codes
The automorphism groups of various linear codes are extensively studied yielding insights into the respective code structure. This knowledge is used in, e.g., theoretical analysis and in improving decoding performance, motivating the analyses of endomorphisms of linear codes. In this work, we discuss the structure of the set of transformation matrices of code endomorphisms, defined as a generalization of code automorphisms, and provide an explicit construction of a bijective mapping between the…

Submanifolds with boundary and Stokes' Theorem in Heisenberg groups
Marco Di Marco, Antoine Julia, Sebastiano Nicolussi Golo, Davide Vittone
https://arxiv.org/abs/2403.18675 <…

Submanifolds with boundary and Stokes' Theorem in Heisenberg groups
We introduce and study the notion of $C^1_\mathbb{H}$-regular submanifold with boundary in sub-Riemannian Heisenberg groups. As an application, we prove a version of Stokes' Theorem for $C^1_\mathbb{H}$-regular submanifolds with boundary that takes into account Rumin's complex of differential forms in Heisenberg groups.

A unique Cartan subalgebra result for Bernoulli actions of weakly amenable groups
Changying Ding
https://arxiv.org/abs/2404.08182 https://

A unique Cartan subalgebra result for Bernoulli actions of weakly amenable groups
We show that if $Γ\curvearrowright (X^Γ,μ^Γ)$ is a Bernoulli action of an i.c.c. nonamenable group $Γ$ which is weakly amenable with Cowling-Haagerup constant $1$, and $Λ\curvearrowright(Y,ν)$ is a free ergodic p.m.p. algebraic action of a group $Λ$, then the isomorphism $L^\infty(X^Γ)\rtimesΓ\cong L^\infty(Y)\rtimesΛ$ implies that $L^\infty(X^Γ)$ and $L^\infty(Y)$ are unitarily conjugate. This is obtained by showing a new rigidity result of non properly proximal groups and combinin…

The border crisis factor no one talks about: #American #guns
One of the main reasons the border has drawn so many migrants and asylum seekers is 🔸the flow of guns from the U.S. into Mexico.🔸
This link between our guns and the people who seek safety at the border is particularly clear in Texas.
Gov. Greg…

The border crisis factor that no one talks about: U.S. guns
The majority of guns in Mexico come from America, supplying the organized crime groups whose violence and drug trafficking drives civilians to seek safety in the U.S.

This https://arxiv.org/abs/2312.15745 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finite almost simple groups whose holomorph contains a solvable regular subgroup
In our previous paper, we gave a complete list of the finite non-abelian simple groups whose holomorph contains a solvable regular subgroup. In this paper, we refine our previous work by considering all finite almost simple groups. In particular, our result yields a complete characterization of the finite almost simple groups which occur as the type of a Hopf-Galois structure on a solvable extension, or equivalently, the additive group of a skew brace having a solvable multiplicative group.

LocalTweets to LocalHealth: A Mental Health Surveillance Framework Based on Twitter Data
Vijeta Deshpande, Minhwa Lee, Zonghai Yao, Zihao Zhang, Jason Brian Gibbons, Hong Yu
https://arxiv.org/abs/2402.13452

LocalTweets to LocalHealth: A Mental Health Surveillance Framework Based on Twitter Data
Prior research on Twitter (now X) data has provided positive evidence of its utility in developing supplementary health surveillance systems. In this study, we present a new framework to surveil public health, focusing on mental health (MH) outcomes. We hypothesize that locally posted tweets are indicative of local MH outcomes and collect tweets posted from 765 neighborhoods (census block groups) in the USA. We pair these tweets from each neighborhood with the corresponding MH outcome reported …

This https://arxiv.org/abs/2212.02249 has been replaced.
link: https://scholar.google.com/scholar?q=a

The symbol length for elementary type pro-$p$ groups and Massey products
For a prime number $p$ and an integer $m\geq2$, we prove that the symbol length of all elements of $m$-fold Massey products in $H^2(G,\mathbb{F}_p)$, for pro-$p$ groups $G$ of elementary type, is bounded by $(m^2/4)+m$. Assuming the Elementary Type Conjecture, this applies to all finitely generated maximal pro-$p$ Galois groups $G=G_F(p)$ of fields $F$ which contain a root of unity of order $p$. More generally, we provide such a uniform bound for the symbol length of all pullbacks $ρ^*(\barω)…

Dihedral-skew product groups of nonabelian simple groups
Hao Yu
https://arxiv.org/abs/2404.15145 https://arxiv.org/pdf/2404.15145

Dihedral-skew product groups of nonabelian simple groups
Given a finite group $G$, a group $X$ is called a dihedral-skew product group of $G$ if $X=GD$ where $G\cap D=1$ and $D$ is a finite dihedral group with trivial core in $X$. In this paper, dihedral-skew product groups of all nonabelian simple groups are classified.

A Szemer\'edi type theorem for sets of positive density in cut-and-project sets
Michael Bj\"orklund, Alexander Fish
https://arxiv.org/abs/2402.17158

A Szemerédi type theorem for sets of positive density in cut-and-project sets
An extension of Szemerédi's Theorem is proved for sets of positive density in cut-and-project sets in general locally compact and second countable abelian groups. As a consequence, we establish a recent conjecture of Klick, Strungaru and Tcaciuc. Furthermore, we show a Szemeredi type theorem for sets of positive density in the set of fractional parts of $\mathbb{Q}_p$. Via a novel version of Furstenberg's Correspondence principle, which should be of independent interest, we show that our Szeme…

This https://arxiv.org/abs/2207.08792 has been replaced.
link: https://scholar.google.com/scholar?q=a

Cohomological invariants and Brauer groups of algebraic stacks in positive characteristic
We introduce a theory of cohomological invariants with mod $p^r$ coefficients for algebraic stacks in characteristic $p$. Using these new tools we complete the computation of the Brauer group and cohomological invariants of the stack of elliptic curves over any field.

Grothendieck's theory of fibred categories for monoids
Ilia Pirashvili
https://arxiv.org/abs/2402.11644 https://arxiv.org/pdf/240…

Grothendieck's theory of fibred categories for monoids
The aim of this paper is to interpret the Grothendieck construction in the monoidal world. That is to say, we restrict the equivalence between fibred categories and pseudo functors to the case of categories having only a single object. On other way of expressing this is to say that we are given a monoid homomorphism. Though only a specialisation, we discover many pleasant results and interpret many things in a new light. We also touch upon the case of finite groups as an example.

This https://arxiv.org/abs/2403.08814 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Solutions of tetrahedron equation from quantum cluster algebra associated with symmetric butterfly quiver
We construct a new solution to the tetrahedron equation by further pursuing the quantum cluster algebra approach in our previous works. The key ingredients include a symmetric butterfly quiver attached to the wiring diagrams for the longest element of type $A$ Weyl groups and the implementation of quantum $Y$-variables through the $q$-Weyl algebra. The solution consists of four products of quantum dilogarithms, incorporating a total of seven parameters. By exploring both the coordinate and mome…

Sandpile groups for cones over trees
Victor Reiner, Dorian Smith
https://arxiv.org/abs/2402.15453 https://arxiv.org/pdf/2402.15453

Sandpile groups for cones over trees
Sandpile groups are a subtle graph isomorphism invariant, in the form of a finite abelian group, whose cardinality is the number of spanning trees in the graph. We study their group structure for graphs obtained by attaching a cone vertex to a tree. For example, it is shown that the number of generators of the sandpile group is at most one less than the number of leaves in the tree. For trees on a fixed number of vertices, the paths and stars are shown to provide extreme behavior, not only for …

This https://arxiv.org/abs/2303.15997 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Burnside problem for odd exponents
We show that the free Burnside groups $B(n,m)$ are infinite for $n\geq 557$ and $m\geq 2$. This is the best currently known lower bound for the exponent. The proof uses iterated small cancellation theory where the induction is based on the nesting depth of relators. The main instrument at every step is a new concept of a certification sequence.

Partial convex hulls of coadjoint orbits and degrees of invariants
Valdemar V. Tsanov
https://arxiv.org/abs/2402.13893 https://arxiv.…

Partial convex hulls of coadjoint orbits and degrees of invariants
We study properties of convex hulls of (co)adjoint orbits of compact groups, with applications to invariant theory and tensor product decompositions. The notion of partial convex hulls is introduced and applied to define two numerical invariants of a coadjoint orbit of a semisimple connected compact Lie group. It is shown that the orbits, where any one of these invariants does not exceed a given number $r$, form, upon intersection with a fixed Weyl chamber, a rational convex polyhedral cone in …

Grothendieck's theory of fibred categories for monoids
Ilia Pirashvili
https://arxiv.org/abs/2402.11644 https://arxiv.org/pdf/240…

Grothendieck's theory of fibred categories for monoids
The aim of this paper is to interpret the Grothendieck construction in the monoidal world. That is to say, we restrict the equivalence between fibred categories and pseudo functors to the case of categories having only a single object. On other way of expressing this is to say that we are given a monoid homomorphism. Though only a specialisation, we discover many pleasant results and interpret many things in a new light. We also touch upon the case of finite groups as an example.

This https://arxiv.org/abs/2307.02085 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finite period vectors and Gauss sums
We study four sums including the Jacquet--Piatetski-Shapiro--Shalika, Flicker, Bump--Friedberg, and Jacquet--Shalika sums associated to irreducible cuspidal representations of general linear groups over finite fields. By computing explicitly, we relate Asai and Bump--Friedberg gamma factors over finite fields to those over nonarchimedean local fields through level zero supercuspidal representation. Via Deligne--Kazhdan close field theory, we prove that exterior square and Bump--Friedberg gamma …

Boundaries and equivariant maps for ergodic groupoids
Filippo Sarti, Alessio Savini
https://arxiv.org/abs/2402.15355 https://arxiv.or…

Boundaries and equivariant maps for ergodic groupoids
We give a notion of boundary pair $(\mathcal{B}_-,\mathcal{B}_+)$ for measured groupoids which generalizes the one introduced by Bader and Furman for locally compact groups. In the case of a semidirect groupoid $\mathcal{G}=Γ\ltimes X$ obtained by a probability measure preserving action $Γ\curvearrowright X$ of a locally compact group, we show that a boundary pair is exactly $(B_- \times X, B_+ \times X)$, where $(B_-,B_+)$ is a boundary pair for $Γ$. For any measured groupoid $(\mathcal{G},…

Symmetry of graphs and perfect state transfer in Grover walks
Sho Kubota, Kiyoto Yoshino
https://arxiv.org/abs/2402.17341 https://arx…

Symmetry of graphs and perfect state transfer in Grover walks
We study relationships between symmetry of graphs and perfect state transfer in Grover walks. Symmetry of graphs mathematically refers to automorphisms of graphs. When perfect state transfer occurs between two vertices, the following two statements hold. One is that automorphisms preserve the occurrence of perfect state transfer. The other is that the stabilizer subgroups of the automorphism groups with respect to those two vertices coincide. Using these results, we completely characterize circ…

Quantum group deformations and quantum $ R $-(co)matrices vs. Quantum Duality Principle
Gast\'on Andr\'es Garc\'ia, Fabio Gavarini
https://arxiv.org/abs/2403.15096

Quantum group deformations and quantum $ R $-(co)matrices vs. Quantum Duality Principle
In this paper we describe the effect on quantum groups - namely, both QUEA's and QFSHA's - of deformations by twist and by 2-cocycles, showing how such deformations affect the semiclassical limit. As a second, more important task, we discuss how these deformation procedures can be "stretched" to a new extent, via a formal variation of the original recipes, using quasi-twists and quasi-2-cocycles. These recipes seemingly should make no sense at all, yet we prove that they actually work, thus p…

Symmetry of graphs and perfect state transfer in Grover walks
Sho Kubota, Kiyoto Yoshino
https://arxiv.org/abs/2402.17341 https://arx…

Symmetry of graphs and perfect state transfer in Grover walks
We study relationships between symmetry of graphs and perfect state transfer in Grover walks. Symmetry of graphs mathematically refers to automorphisms of graphs. When perfect state transfer occurs between two vertices, the following two statements hold. One is that automorphisms preserve the occurrence of perfect state transfer. The other is that the stabilizer subgroups of the automorphism groups with respect to those two vertices coincide. Using these results, we completely characterize circ…

Asymptotic behaviour of holomorphic extensions of matrix coefficients at the boundary of the complex crown domain
Tobias Simon
https://arxiv.org/abs/2403.13572

Asymptotic behaviour of holomorphic extensions of matrix coefficients at the boundary of the complex crown domain
In this paper, we provide a simpler proof of the Krötz--Stanton Extension Theorem for holomorphic extensions of orbit maps in unitary irreducible representations of connected semisimple Lie groups. Our result is a generalization of the previous result as it applies to Hilbert globalizations of finitely generated admissible $(\mathfrak{g},K)$-modules for arbitrary connected semisimple Lie groups $G$ with not necessarily finite center. Furthermore, we give polynomial growth estimates for the nor…

NY appellate court greenlights challenge of #crypto-mining power plant | Courthouse News Service
https://www.courthousenews.com/new-york-a…

NY appellate court greenlights challenge of crypto-mining power plant
Environmental groups claim that the project would increase the power plant’s emissions by up to 3,500%.

This https://arxiv.org/abs/2306.13635 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Factoring determinants and applications to number theory
Products of shifted characteristic polynomials, and ratios of such products, averaged over the classical compact groups are of great interest to number theorists as they model similar averages of L-functions in families with the same symmetry type as the compact group. We use Toeplitz and Toeplitz plus Hankel operators and the identities of Borodin - Okounkov, Case - Geronimo, and Basor - Erhardt to prove that, in certain cases, these unitary averages factor as polynomials in the matrix size in…

The Leibniz PROP is a crossed presimplicial algebra
Murat Can A\c{s}karo\u{g}ullar{\i}, Atabey Kaygun
https://arxiv.org/abs/2404.10925 https://

The Leibniz PROP is a crossed presimplicial algebra
We prove that the Leibniz PROP is isomorphic (as $\Bbbk$-linear categories) to the symmetric crossed presimplicial algebra $\Bbbk[(Δ^+)^{op} \mathbb{S}]$ where $Δ^+$ is the skeletal category of finite well-ordered sets with surjections, but the distributive law between $(Δ^+)^{op}$ and the symmetric groups $\mathbb{S} = \bigsqcup_{n\geq 1} S_n$ is not the standard one.

Cosystolic Expansion of Sheaves on Posets with Applications to Good 2-Query LTCs and Lifted Codes
Uriya A. First, Tali Kaufman
https://arxiv.org/abs/2403.19388

Cosystolic Expansion of Sheaves on Posets with Applications to Good 2-Query LTCs and Lifted Codes
We study sheaves on posets, showing that cosystolic expansion of such sheaves can be derived from local expansion conditions of the sheaf and the poset (typically a high dimensional expander). When the poset at hand is a cell complex, a sheaf on it may be thought of as generalizing coefficient groups used for defining homology and cohomology, by letting the coefficient group vary along the cell complex. Previous works established local criteria for cosystolic expansion only for simplicial compl…

#WhiteSupremacists forming "fitness clubs," slam #Trump's blubber - National Zero

Arc-transitive maps with coprime Euler characteristic and edge number
C. H. Li, Lu Yi Liu
https://arxiv.org/abs/2403.18335 https://ar…

Arc-transitive maps with coprime Euler characteristic and edge number
This is one of a series of papers which aim towards a classification of edge-transitive maps of which the Euler characteristic and the edge number are coprime. This one carries out the classification work for arc-transitive maps with nonsolvable automorphism groups, which illustrates how the edge number impacts on the Euler characteristic for maps. The classification is involved with the construction of some new and interesting arc-regular maps.

This https://arxiv.org/abs/2402.19074 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Dynamical Systems on Compact Metrizable Groups
This paper is aim to extend Kenneth R. Berg's findings on the maximal entropy theorem and the ergodicity of measure convolution to the case of surjective homomorphisms. We further explores dynamical systems under surjective homomorphism in detail, especially the variation of entropy. Let $G_{1} $ and $G_{2} $ be compact metrizable groups, and suppose that $G_{2} $ acts freely on $G_{1} $, the continuous mapping $T_{1} $ and homomorphism $T_{2} :G_{2} \to G_{2} $ satisfy $T_{1} (yx)=T_{2} (y)T…

On the character tables of the finite reductive groups $E_6(q)_{\text{ad}}$ and ${^2\!E}_6(q)_{\text{ad}}$
Meinolf Geck
https://arxiv.org/abs/2403.02434 ht…

On the character tables of the finite reductive groups $E_6(q)_{\text{ad}}$ and ${^2\!E}_6(q)_{\text{ad}}$
We show how the character tables of the groups $E_6(q)_{\text{ad}}$ and ${^2\!E}_6(q)_{\text{ad}}$ can be constructed, where $q$ is a power of~$2$. (Partial results are also obtained for the case where $q$ is a power of any prime $\neq 3$.) This is based on previous work by Hetz, Lusztig, Malle, Mizuno and Shoji, plus some computations using Michel's version of {\sf CHEVIE}. We also need some general results that are specific to groups where centralisers of semisimple elements are possibly not …

This https://arxiv.org/abs/2310.16286 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Homological stability for generalized Hurwitz spaces and Selmer groups in quadratic twist families over function fields
We prove a version of the Bhargava-Kane-Lenstra-Poonen-Rains heuristics for Selmer groups of quadratic twist families of abelian varieties over global function fields. As a consequence, we derive a result towards the "minimalist conjecture" on Selmer ranks of abelian varieties in such families. More precisely, we show that the probabilities predicted in these two conjectures are correct to within an error term in the size of the constant field, $q$, which goes to $0$ as $q$ grows. Two key input…

Haar graphical representations of finite groups and an application to poset representations
Joy Morris, Pablo Spiga
https://arxiv.org/abs/2404.12658 https:…

Haar graphical representations of finite groups and an application to poset representations
Let $R$ be a group and let $S$ be a subset of $R$. The Haar graph $\mathrm{Haar}(R,S)$ of $R$ with connection set $S$ is the graph having vertex set $R\times\{-1,1\}$, where two distinct vertices $(x,-1)$ and $(y,1)$ are declared to be adjacent if and only if $yx^{-1}\in S$. The name Haar graph was coined by Tomaž Pisanski in one of the first investigations on this class of graphs. For every $g\in R$, the mapping $ρ_g:(x,\varepsilon)\mapsto (xg,\varepsilon)$, $\forall (x,\varepsilon)\in R\t…

Classifying abelian groups through acyclic matchings
Mohsen Aliabadi, Peter Taylor
https://arxiv.org/abs/2402.08008 https://arxiv.org…

Classifying abelian groups through acyclic matchings
The inquiry into identifying sets of monomials that can be eliminated from a generic homogeneous polynomial via a linear change of coordinates was initiated by E. K. Wakeford in [10]. This linear algebra problem prompted C. K. Fan and J. Losonczy to introduce the notion of acyclic matchings in the additive group $\mathbb{Z}^n$ in [5], subsequently extended to abelian groups by the latter author[9]. Alon et al., in [4], established the acyclic matching property for $\mathbb{Z}^n$. This note aims…

Representations from matrix varieties, and filtered RSK
Abigail Price, Ada Stelzer, Alexander Yong
https://arxiv.org/abs/2403.09938 https://

Representations from matrix varieties, and filtered RSK
Matrix Schubert varieties (Fulton '92) carry natural actions of Levi groups. Their coordinate rings are thereby Levi-representations; what is a combinatorial counting rule for the multiplicities of their irreducibles? When the Levi group is a torus, (Knutson-Miller '04) answers the question. We present a general solution, a common refinement of the multigraded Hilbert series, the Cauchy identity, and the Littlewood-Richardson rule. Our result applies to any ``bicrystalline'' algebraic variety; …

Simple Tilings of Nilpotent Lie Groups
Kyle Hansen
https://arxiv.org/abs/2402.10194 https://arxiv.org/pdf/2402.10194

Simple Tilings of Nilpotent Lie Groups
We define simple tilings in the general context of a G-tiling on a Riemannian homogeneous space M to be tilings by "almost linear" simplices. As evidence that this definition is natural, we prove that a natural class of tilings of M are MLD to simple ones. We demonstrate the utility of this definition by generalizing previously known results about simple tilings of Euclidean space. In particular, it is shown that a simple tiling space of a connected, simply connected, rational, nilpotent Lie gr…

Spread Construction for (36,15,6) Hadamard Difference Sets
Ken Smith, Jordan Webster
https://arxiv.org/abs/2402.08503 https://arxiv.o…

Spread Construction for (36,15,6) Hadamard Difference Sets
There are exactly 35 inequivalent (36, 15, 6) difference sets in nine groups. Eight of the nine groups have a normal Sylow 3-subgroup. We give a straightforward spread construction which explains the 32 inequivalent difference sets in these eight groups. An interesting variation on this construction provides the three difference sets in the ninth group.

Test for amenability for extensions of infinite residually finite groups
Mar\'ia Isabel Cortez, Jaime G\'omez
https://arxiv.org/abs/2403.06982 http…

Test for amenability for extensions of infinite residually finite groups
Let $G$ be a countable group that admits a minimal equicontinuous action on the Cantor set (for example, a residually finite group). We show that the family of almost automorphic actions of $G$ on the Cantor set, is a test for amenability for $G$. More precisely, we show that if $G$ is non-amenable, then for every minimal equicontinuous system $(Y, G)$, such that $Y$ is a Cantor set, there exists a Toeplitz subshift with no invariant probability measures, whose maximal equicontinuous factor is …

Self-Avoiding Walks on Cayley Graphs Through the Lens of Symbolic Dynamics
Nathalie Aubrun, Nicol\'as Bitar
https://arxiv.org/abs/2402.13944 https://…

Self-Avoiding Walks on Cayley Graphs Through the Lens of Symbolic Dynamics
We study dynamical and computational properties of the set of bi-infinite self-avoiding walks on Cayley graphs, as well as ways to compute, approximate and bound their connective constant. To do this, we introduce the skeleton $X_{G,S}$ of a finitely generated group $G$ relative to a generating set $S$, which is a one-dimensional subshift made of configurations on $S$ that avoid all words that reduce to the identity. We provide a characterization of groups which have SFT skeletons and sofic ske…

This https://arxiv.org/abs/2307.04698 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Khintchine-type double recurrence in abelian groups
We prove a Khintchine-type recurrence theorem for pairs of endomorphisms of a countable discrete abelian group. As a special case of the main result, if $Γ$ is a countable discrete abelian group, $φ, ψ\in End(Γ)$, and $ψ- φ$ is an injective endomorphism with finite index image, then for any ergodic measure-preserving $Γ$-system $\left( X, \mathcal{X}, μ, (T_g)_{g \in Γ} \right)$, any measurable set $A \in \mathcal{X}$, and any $\varepsilon > 0$, the set of $g \in Γ$ for which $$μ\lef…

Homotopy type of shellable $q$-complexes and their homology groups
Sudhir R. Ghorpade, Rakhi Pratihar, Tovohery H. Randrianarisoa, Hugues Verdure, Glen Wilson
https://arxiv.org/abs/2403.07102

Homotopy type of shellable $q$-complexes and their homology groups
The theory of shellable simplicial complexes brings together combinatorics, algebra, and topology in a remarkable way. Initially introduced by Alder for $q$-simplicial complexes, recent work of Ghorpade, Pratihar, and Randrianarisoa extends the study of shellability to $q$-matroid complexes and determines singular homology groups for a subclass of these $q$-simplicial complexes. In this paper, we determine the homotopy type of shellable $q$-simplicial complexes. Moreover, we establish the shell…

PySymmPol: Symmetric Polynomials in Python
Thiago Araujo
https://arxiv.org/abs/2403.13580 https://arxiv.org/pdf/2403.13580

PySymmPol: Symmetric Polynomials in Python
PySymmPol is a Python package designed for efficient manipulation of symmetric polynomials. It provides functionalities for working with various types of symmetric polynomials, including elementary, homogeneous, monomial symmetric, (skew-) Schur, and Hall-Littlewood polynomials. In addition to polynomial operations, PySymmPol offers tools to explore key properties of integer partitions and Young diagrams, such as transposition, Frobenius coordinates, characters of symmetric groups and others.

Eulerian magnitude homology: subgraph structure and random graphs
Chad Giusti, Giuliamaria Menara
https://arxiv.org/abs/2403.09248 https://

Eulerian magnitude homology: subgraph structure and random graphs
In this paper we explore the connection between the ranks of the magnitude homology groups of a graph and the structure of its subgraphs. To this end, we introduce variants of magnitude homology called eulerian magnitude homology and discriminant magnitude homology. Leveraging the combinatorics of the differential in magnitude homology, we illustrate a close relationship between the ranks of the eulerian magnitude homology groups on the first diagonal and counts of subgraphs which fall in speci…

Eulerian magnitude homology: subgraph structure and random graphs
Chad Giusti, Giuliamaria Menara
https://arxiv.org/abs/2403.09248 https://

Eulerian magnitude homology: subgraph structure and random graphs
In this paper we explore the connection between the ranks of the magnitude homology groups of a graph and the structure of its subgraphs. To this end, we introduce variants of magnitude homology called eulerian magnitude homology and discriminant magnitude homology. Leveraging the combinatorics of the differential in magnitude homology, we illustrate a close relationship between the ranks of the eulerian magnitude homology groups on the first diagonal and counts of subgraphs which fall in speci…

Sets of Cross Numbers of Sequences over Finite Abelian Groups
Aqsa Bashir, Wolfgang A. Schmid
https://arxiv.org/abs/2403.07138 https://

Sets of Cross Numbers of Sequences over Finite Abelian Groups
Let $G$ be a finite abelian group with $\exp(G)$ the exponent of $G$. Then $\mathsf W(G)$ denotes the set of cross numbers of minimal zero-sum sequences over $G$ and $\mathsf w(G)$ denotes the set of all cross numbers of non-trivial zero-sum free sequences over $G$. It is clear that $\mathsf W(G)$ and $\mathsf w(G)$ are bounded subsets of $\frac{1}{\exp(G)}\mathbb{N}$ with maximum $ \mathsf K(G)$ and $\mathsf k(G)$, respectively (here $\mathsf{K}(G)$ and $\mathsf{k}(G)$ denote the large and the…

Disarray, reduced words, and 321-avoidance in George groups
Joel Brewster Lewis, Bridget Eileen Tenner
https://arxiv.org/abs/2404.06379 https://

Disarray, reduced words, and 321-avoidance in George groups
Previous work has shown that the disarray (or displacement) of an (affine) (signed) permutation is bounded in terms of its Coxeter length. Here, we characterize the permutations for which the bound is sharp in two ways: in terms of a natural property of their reduced words, and by ``globally'' avoiding the pattern 321.

This https://arxiv.org/abs/2401.15456 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Product Mixing in Compact Lie Groups
If $G$ is a group, we say a subset $S$ of $G$ is product-free if the equation $xy=z$ has no solutions with $x,y,z \in S$. For $D \in \mathbb{N}$, a group $G$ is said to be $D$-quasirandom if the minimal dimension of a nontrivial complex irreducible representation of $G$ is at least $D$. Gowers showed that in a $D$-quasirandom finite group $G$, the maximal size of a product-free set is at most $|G|/D^{1/3}$. This disproved a longstanding conjecture of Babai and Sós from 1985. For th…

0-Hecke Modules, Domino Tableaux, and Type-$B$ Quasisymmetric Functions
Colin Defant, Dominic Searles
https://arxiv.org/abs/2404.04961 https://

0-Hecke Modules, Domino Tableaux, and Type-$B$ Quasisymmetric Functions
We extend the notion of ascent-compatibility from symmetric groups to all Coxeter groups, thereby providing a type-independent framework for constructing families of modules of $0$-Hecke algebras. We apply this framework in type $B$ to give representation-theoretic interpretations of a number of noteworthy families of type-$B$ quasisymmetric functions. Next, we construct modules of the type-$B$ $0$-Hecke algebra corresponding to type-$B$ analogues of Schur functions and introduce a type-$B$ ana…

Genus and crosscap of Normal subgroup based power graphs of finite groups
Parveen, Manisha, Jitender Kumar
https://arxiv.org/abs/2404.03895 https://

Genus and crosscap of Normal subgroup based power graphs of finite groups
Let $H$ be a normal subgroup of a group $G$. The normal subgroup based power graph $Γ_H(G)$ of $G$ is the simple undirected graph with vertex set $V(Γ_H(G))= (G\setminus H)\cup \{e\}$ and two distinct vertices $a$ and $b$ are adjacent if either $aH = b^m H$ or $bH=a^nH$ for some $m,n \in \mathbb{N}$. In this paper, we continue the study of normal subgroup based power graph and characterize all the pairs $(G,H)$, where $H$ is a non-trivial normal subgroup of $G$, such that the genus of $Γ_H(G…

The restricted sumsets in finite abelian groups
Shanshan Du, Hao Pan
https://arxiv.org/abs/2403.03549 https://arxiv.org/pdf/2403.0354…

The restricted sumsets in finite abelian groups
Suppose that $k\geq 2$ and $A$ is a non-empty subset of a finite abelian group $G$ with $|G|>1$. Then the cardinality of the restricted sumset $$ k^\wedge A:=\{a_1+\cdots+a_k:\,a_1,\ldots,a_k\in A,\ a_i\neq a_j\text{ for }i\neq j\} $$ is at least $$ \min\{p(G), k|A|-k^2+1\}, $$ where $p(G)$ denotes the least prime divisor of $|G|$.

The restricted sumsets in finite abelian groups
Shanshan Du, Hao Pan
https://arxiv.org/abs/2403.03549 https://arxiv.org/pdf/2403.0354…

The restricted sumsets in finite abelian groups
Suppose that $k\geq 2$ and $A$ is a non-empty subset of a finite abelian group $G$ with $|G|>1$. Then the cardinality of the restricted sumset $$ k^\wedge A:=\{a_1+\cdots+a_k:\,a_1,\ldots,a_k\in A,\ a_i\neq a_j\text{ for }i\neq j\} $$ is at least $$ \min\{p(G), k|A|-k^2+1\}, $$ where $p(G)$ denotes the least prime divisor of $|G|$.

Boolean intervals in the weak Bruhat order of a finite Coxeter group
Ben Adenbaum, Jennifer Elder, Pamela E. Harris, J. Carlos Mart\'inez Mori
https://arxiv.org/abs/2403.07989

Boolean intervals in the weak Bruhat order of a finite Coxeter group
Given a Coxeter group $W$ with Coxeter system $(W,S)$, where $S$ is finite. We provide a complete characterization of Boolean intervals in the weak order of $W$ uniformly for all Coxeter groups in terms of independent sets of the Coxeter graph. Moreover, we establish that the number of Boolean intervals of rank $k$ in the weak order of $W$ is ${i_k(Γ_W)\cdot|W|}\,/\,2^{k}$, where $Γ_W$ is the Coxeter graph of $W$ and $i_k(Γ_W)$ is the number of independent sets of size $k$ of $Γ_W…