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lesmis: Les Misérables coappearances
The network of scene coappearances of characters in Victor Hugo's novel "Les Miserables". Edge weights denote the number of such occurrences.
This network has 77 nodes and 254 edges.
Tags: Social, Fictional, Weighted
https://networks.skewed.de/net/lesmis

On Modified Diagonal Cycles and the Beauville Decomposition of the Ceresa Cycle
Lucas Lagarde, Mohamed Moakher, Morena Porzio, James Rawson, Fernando Trejos Su\'arez
https://arxiv.org/abs/2510.07416

On Modified Diagonal Cycles and the Beauville Decomposition of the Ceresa Cycle
Let $C$ be a curve of genus $g \geq 2$, and let $J$ be its Jacobian. The choice of a degree 1 divisor $e$ on $C$ gives an embedding of $C$ into $J$; we denote by $[C]_{}^{e}\in \mathrm{CH}\left( J;\mathbb{Q} \right) $ the class in the Chow group of $J$ defined by the image of this embedding. It is known from the work of S.-W. Zhang that the vanishing of the Ceresa cycle $\mathrm{Cer}(C,e):=[C]^{e} - [-1]_* [C]^e$ is equivalent to both the vanishing of the 1st Beauville component $[C]_{(1)}^e$ a…

student_cooperation: Student cooperation (2012)
Network of cooperation among students in the "Computer and Network Security" course at Ben-Gurion University, in 2012. Nodes are students, and edges denote cooperation between students while doing their homework. The graph contains three types of links: Time, Computer, Partners.
This network has 185 nodes and 360 edges.
Tags: Social, Offline, Multigraph, Unweighted

student_cooperation: Student cooperation (2012)
Network of cooperation among students in the "Computer and Network Security" course at Ben-Gurion University, in 2012. Nodes are students, and edges denote cooperation between students while doing their homework. The graph contains three types of links: Time, Computer, Partners.
This network has 185 nodes and 360 edges.
Tags: Social, Offline, Multigraph, Unweighted

student_cooperation: Student cooperation (2012)
Network of cooperation among students in the "Computer and Network Security" course at Ben-Gurion University, in 2012. Nodes are students, and edges denote cooperation between students while doing their homework. The graph contains three types of links: Time, Computer, Partners.
This network has 185 nodes and 360 edges.
Tags: Social, Offline, Multigraph, Unweighted

Bounded powers of edge ideals: Gorenstein polytopes
Takayuki Hibi, Seyed Amin Seyed Fakhari
https://arxiv.org/abs/2510.11668 https://arxiv.org/pdf/2510.116…

Bounded powers of edge ideals: Gorenstein polytopes
Let $S=K[x_1, \ldots,x_n]$ denote the polynomial ring in $n$ variables over a field $K$ and $I(G) \subset S$ the edge ideal of a finite graph $G$ on $n$ vertices. Given a vector $\mathfrak{c}\in\mathbb{N}^n$ and an integer $q\geq 1$, we denote by $(I(G)^q)_{\mathfrak{c}}$ the ideal of $S$ generated by those monomials belonging to $I(G)^q$ whose exponent vectors are componentwise bounded above by $\mathfrak{c}$. Let $δ_{\mathfrak{c}}(I(G))$ denote the largest integer $q$ for which $(I(G)^q)_{\m…

lesmis: Les Misérables coappearances
The network of scene coappearances of characters in Victor Hugo's novel "Les Miserables". Edge weights denote the number of such occurrences.
This network has 77 nodes and 254 edges.
Tags: Social, Fictional, Weighted
https://networks.skewed.de/net/lesmis

lesmis: Les Misérables coappearances
The network of scene coappearances of characters in Victor Hugo's novel "Les Miserables". Edge weights denote the number of such occurrences.
This network has 77 nodes and 254 edges.
Tags: Social, Fictional, Weighted
https://networks.skewed.de/net/lesmis

A note on the number of non-cycle components in a pseudo 2-factor of graphs
Masaki Kashima
https://arxiv.org/abs/2510.12155 https://arxiv.org/pdf/2510.1215…

A note on the number of non-cycle components in a pseudo 2-factor of graphs
A pseudo 2-factor of a graph is a spanning subgraph such that each component is $K_1$, $K_2$, or a cycle. This notion was introduced by Bekkai and Kouider in 2009, where they showed that every graph $G$ has a pseudo 2-factor with at most $α(G)-δ(G)+1$ components that are not cycles. For a graph $G$ and a set of vertices $S$, let $δ_G(S)$ denote the minimum degree of vertices in $S$. In this note, we show that every graph $G$ has a pseudo 2-factor with at most $f(G)$ components that are not c…

A preorder on the set of links defined via orbifolds
Michel Boileau, Teruaki Kitano, Yuta Nozaki
https://arxiv.org/abs/2510.12372 https://arxiv.org/pdf/251…

A preorder on the set of links defined via orbifolds
For a link $L$ in the $3$-sphere, the $π$-orbifold group $G^\mathrm{orb}(L)$ is defined as a quotient of the link group of $L$. When there exists an epimorphism $G^\mathrm{orb}(L)\to G^\mathrm{orb}(L')$, we denote this by $L\succeq L'$ and explore the relationships between the two links. Specifically, we prove that if $L\succeq L'$ and $L$ is a Montesinos link with $r$ rational tangles $(r\geq 3)$, then $L'$ is either a Montesinos link with at most $r+1$ rational tangles or a certain connected…

lesmis: Les Misérables coappearances
The network of scene coappearances of characters in Victor Hugo's novel "Les Miserables". Edge weights denote the number of such occurrences.
This network has 77 nodes and 254 edges.
Tags: Social, Fictional, Weighted
https://networks.skewed.de/net/lesmis

Automorphism Orbits of the Group of Unitriangular Matrices
Emerson de Melo, J\'ulia Kato
https://arxiv.org/abs/2510.09353 https://arxiv.org/pdf/2510.09…

Automorphism Orbits of the Group of Unitriangular Matrices
Let $G$ be a group. The orbits of the natural action of $Aut(G)$ on $G$ are called the automorphism orbits of $G$, and their number is denoted by $ω(G)$. Let $\mathbb{F}$ be an infinite field, and let $UT_n(\mathbb{F})$ denote the group of unitriangular matrices over $\mathbb{F}$. We show that $ω(UT_n(\mathbb{F}))$ is finite for $n \leq 5$ and infinite for $n \geq 6$.

Twists arising from torsion points
Lukas Novak
https://arxiv.org/abs/2510.08486 https://arxiv.org/pdf/2510.08486 …

Twists arising from torsion points
Let $p$ be a prime number, $K$ a number field that contains the $p$-th root of unity $ζ_p$, $d$ a $p$-power-free integer and $L=K(\sqrt[p]{d})$. Let $E/K$ be an elliptic curve with full $p$-torsion and $S,T \in E(K)[p]$ be the generators. Define the cocycle $ξ_d : \operatorname{Gal}(\overline{K}/K) \to E$ by \[ ξ_d (σ)= \begin{cases} O, & \text{if } σ(\sqrt[p]{d})=\sqrt[p]{d}, \newline kS, & \text{if } σ(\sqrt[p]{d})=ζ_p^k\sqrt[p]{d}, \end{cases} \] and denote by $H_S^d$ the twist …

On real functions with graphs either connected or locally connected
Gerald Kuba
https://arxiv.org/abs/2510.12450 https://arxiv.org/pdf/2510.12450

On real functions with graphs either connected or locally connected
Let S denote the family of all subspaces of the plane that are graphs of functions from the real line R to itself. We prove that S has two subfamilies G,H of spaces such that the cardinality of G is c (the cardinality of the continuum) and the cardinality of H is 2^c, every space in the family G is completely metrizable, each element of H is a dense subset of the plane and the elements of the union of G and H are pairwise non-embeddable (i.p. pairwise non-homeomorphic) subspaces of the plane. O…

student_cooperation: Student cooperation (2012)
Network of cooperation among students in the "Computer and Network Security" course at Ben-Gurion University, in 2012. Nodes are students, and edges denote cooperation between students while doing their homework. The graph contains three types of links: Time, Computer, Partners.
This network has 185 nodes and 360 edges.
Tags: Social, Offline, Multigraph, Unweighted

Precise convergence rate of spectral radius of product of complex Ginibre
Yutao Ma, Xujia Meng
https://arxiv.org/abs/2510.07942 https://arxiv.org/pdf/2510.…

Precise convergence rate of spectral radius of product of complex Ginibre
Let $Z_1, \cdots, Z_n$ denote the eigenvalues of the product $\prod_{j=1}^{k_n} \boldsymbol{A}_j$, where $\{\boldsymbol{A}_j\}_{1 \le j \le k_n}$ are independent $n\times n$ complex Ginibre matrices. Define $α= \lim\limits_{n \to \infty} \frac{n}{k_n}$. We prove that $X_n,$ a suitably rescaled version of $\max_{1 \le j \le n} |Z_j|^2,$ converges weakly as follows: to a non-trivial distribution $Φ_α$ for $α\in (0, +\infty)$, to the Gumbel distribution when $α= +\infty$, and to the…

Inequalities, identities, and bounds for divided differences of the exponential function
Qiulin Zeng, Nicholas Ezzell, Arman Babakhani, Itay Hen, Lev Barash
https://arxiv.org/abs/2510.10724

Inequalities, identities, and bounds for divided differences of the exponential function
Let $\exp[x_0,x_1,\dots,x_n]$ denote the divided difference of the exponential function. (i) We prove that exponential divided differences are log-submodular. (ii) We establish the four-point inequality $ \exp[a,a,b,c]\,\exp[d,d,b,c]+\exp[b,b,a,d]\,\exp[c,c,a,d]-\exp[a,b,c,d]^2 \ge 0 $ for all $ a,b,c,d \in \mathbb{R} $. (iii) We obtain sharp two-sided bounds for $\exp[x_0,\dots,x_n]$ at fixed mean and variance; as a consequence, we derive their large-input asymptotics. (iv) We present …

lesmis: Les Misérables coappearances
The network of scene coappearances of characters in Victor Hugo's novel "Les Miserables". Edge weights denote the number of such occurrences.
This network has 77 nodes and 254 edges.
Tags: Social, Fictional, Weighted
https://networks.skewed.de/net/lesmis

student_cooperation: Student cooperation (2012)
Network of cooperation among students in the "Computer and Network Security" course at Ben-Gurion University, in 2012. Nodes are students, and edges denote cooperation between students while doing their homework. The graph contains three types of links: Time, Computer, Partners.
This network has 185 nodes and 360 edges.
Tags: Social, Offline, Multigraph, Unweighted

On the Coarse Lusternik-Schnirelmann Category of Groups
Aditya De Saha
https://arxiv.org/abs/2510.10367 https://arxiv.org/pdf/2510.10367

On the Coarse Lusternik-Schnirelmann Category of Groups
We introduce a coarse analog of the classical Lusternik-Schnirelmann category which we denote by $\text{c-cat}$, defined for metric spaces in the coarse homotopy category. This provides a new tool for studying large-scale topological properties of groups and spaces. We establish that $\text{c-cat}$ is a coarse homotopy invariant and prove a lower-bound $\text{p-cat}(Γ)\leq \text{c-cat}(Γ)$ for geometrically finite groups $Γ$, where $\text{p-cat}$ denotes the proper LS-category introduced in …

student_cooperation: Student cooperation (2012)
Network of cooperation among students in the "Computer and Network Security" course at Ben-Gurion University, in 2012. Nodes are students, and edges denote cooperation between students while doing their homework. The graph contains three types of links: Time, Computer, Partners.
This network has 185 nodes and 360 edges.
Tags: Social, Offline, Multigraph, Unweighted

Longest paths in trees and isometricity of ultrametric spaces
Oleksiy Dovgoshey, Olga Rovenska
https://arxiv.org/abs/2510.10038 https://arxiv.org/pdf/2510.…

Longest paths in trees and isometricity of ultrametric spaces
Let $T$ be a tree of arbitrary finite or infinite order and let $U(T)$ be the set of all ultrametric spaces generated by vertex labelings of $T$. Let ${\bf US}$ denote the class of all ultrametric spaces generated by vertex labelings of star graphs. We prove that the inclusion $U(T)\subseteq {\bf US}$ holds if and only if the longest path in $T$ has a length not exceeding three.

yahoo_song: Yahoo song ratings (2011)
A bipartite network of users and songs they rated, as used in the 2011 KDD Cup and extracted from Yahoo! Music. Edge weights denote a rating scaled from 0 to 100. More information about this data set is available at http://konect.cc/networks/yahoo-song.
Th…

yahoo_song: Yahoo song ratings (2011)
A bipartite network of users and songs they rated, as used in the 2011 KDD Cup and extracted from Yahoo! Music. Edge weights denote a rating scaled from 0 to 100. More information about this data set is available at http://konect.cc/networks/yahoo-song.
Th…

yahoo_song: Yahoo song ratings (2011)
A bipartite network of users and songs they rated, as used in the 2011 KDD Cup and extracted from Yahoo! Music. Edge weights denote a rating scaled from 0 to 100. More information about this data set is available at http://konect.cc/networks/yahoo-song.
Th…

student_cooperation: Student cooperation (2012)
Network of cooperation among students in the "Computer and Network Security" course at Ben-Gurion University, in 2012. Nodes are students, and edges denote cooperation between students while doing their homework. The graph contains three types of links: Time, Computer, Partners.
This network has 185 nodes and 360 edges.
Tags: Social, Offline, Multigraph, Unweighted

Transitivities of maps of generalized topological spaces
M. R. Ahmadi Zand, N. Baimani
https://arxiv.org/abs/2511.06241 https://arxiv.org/pdf/2511.06241 https://arxiv.org/html/2511.06241
arXiv:2511.06241v1 Announce Type: new
Abstract: In this work, we present several new findings regarding the concepts of orbit-transitivity, strict orbit-transitivity, $\omega$-transitivity, and $\mu$-open-set transitivity for self-maps on generalized topological spaces.
Let $(X,\mu)$ denote a generalized topological space. A point $x \in X$ is said to be \textit{quasi-$\mu$-isolated} if there exists a $\mu$-open set $U$ such that $x \in U$ and $i_\mu(U \setminus c_\mu(\{x\})) = \emptyset$. We prove that $x$ is a quasi-$\mu$-isolated point of $X$ precisely when there exists a $\mu$-dense subset $D$ of $X$ for which $x$ is a $\mu_D$-isolated point of $D$. Moreover, in the case where $X$ has no quasi-$\mu$-isolated points, we establish that a map $f: X \to X$ is orbit-transitive (or strictly orbit-transitive) if and only if it is $\omega$-transitive.
toXiv_bot_toot

lesmis: Les Misérables coappearances
The network of scene coappearances of characters in Victor Hugo's novel "Les Miserables". Edge weights denote the number of such occurrences.
This network has 77 nodes and 254 edges.
Tags: Social, Fictional, Weighted
https://networks.skewed.de/net/lesmis

student_cooperation: Student cooperation (2012)
Network of cooperation among students in the "Computer and Network Security" course at Ben-Gurion University, in 2012. Nodes are students, and edges denote cooperation between students while doing their homework. The graph contains three types of links: Time, Computer, Partners.
This network has 185 nodes and 360 edges.
Tags: Social, Offline, Multigraph, Unweighted

lesmis: Les Misérables coappearances
The network of scene coappearances of characters in Victor Hugo's novel "Les Miserables". Edge weights denote the number of such occurrences.
This network has 77 nodes and 254 edges.
Tags: Social, Fictional, Weighted
https://networks.skewed.de/net/lesmis

student_cooperation: Student cooperation (2012)
Network of cooperation among students in the "Computer and Network Security" course at Ben-Gurion University, in 2012. Nodes are students, and edges denote cooperation between students while doing their homework. The graph contains three types of links: Time, Computer, Partners.
This network has 185 nodes and 360 edges.
Tags: Social, Offline, Multigraph, Unweighted

lesmis: Les Misérables coappearances
The network of scene coappearances of characters in Victor Hugo's novel "Les Miserables". Edge weights denote the number of such occurrences.
This network has 77 nodes and 254 edges.
Tags: Social, Fictional, Weighted
https://networks.skewed.de/net/lesmis

yahoo_song: Yahoo song ratings (2011)
A bipartite network of users and songs they rated, as used in the 2011 KDD Cup and extracted from Yahoo! Music. Edge weights denote a rating scaled from 0 to 100. More information about this data set is available at http://konect.cc/networks/yahoo-song.
Th…

yahoo_song: Yahoo song ratings (2011)
A bipartite network of users and songs they rated, as used in the 2011 KDD Cup and extracted from Yahoo! Music. Edge weights denote a rating scaled from 0 to 100. More information about this data set is available at http://konect.cc/networks/yahoo-song.
Th…

yahoo_song: Yahoo song ratings (2011)
A bipartite network of users and songs they rated, as used in the 2011 KDD Cup and extracted from Yahoo! Music. Edge weights denote a rating scaled from 0 to 100. More information about this data set is available at http://konect.cc/networks/yahoo-song.
Th…