Circuit partitions and signed interlacement in 4-regular graphs
Lafayette College（拉法耶特学院）
Lorenzo Traldi
备注：
v1: 26 pages. v2: 26 pages; many small improvements. v3: 27 pages; minor corrections and changes in notation. v4: 28 pages, 3 figures; minor improvements. v5: 28 pages, 3 figures; minor improvements. v6: 28 pages, 3 figures; minor improvements. v7: 28 pages, 3 figures; updated references. v8: 25 pages, 4 figures. Further changes may be made before publication in Contrib. Discrete Math
发表信息：
Contributions to Discrete Mathematics 20 (2025), 456-480
Let $F$ be a 4-regular graph. Each circuit partition $P$ of $F$ has a corresponding touch-graph $Tch(P)$; the circuits in $P$ correspond to vertices of $Tch(P)$, and the vertices of $F$ correspond to edges of $Tch(P)$. We discuss the connection between modified versions of the interlacement matrix of an Euler system of $F$ and the cycle space of $Tch(P)$, over $GF(2)$ and $\mathbb{R}$.
Some combinatorics related to central binomial coefficients: Grand-Dyck paths, coloured noncrossing partitions and signed pattern avoiding permutations
Signed Counting on Restricted Partitions and Combinatorial Proofs of Three Identities
College of Mathematics and Statistics & Center for Discrete Mathematics, Chongqing University（重庆大学数学与统计学院与离散数学中心）；College of Mathematics and Statistics, Chongqing University（重庆大学数学与统计学院）
Signed Hultman Numbers and Signed Generalized Commuting Probability in Finite Groups
Let G be a finite group . Let pi be a permutation from S{n}. We study the distribution of probabilities of equality a{1} a{2} ...a{n-1}a{n}=a{pi{1}}^{epsilon{1}} a{ pi_{2} }^{epsilon{2}}...a{pi{n-1}}^{ epsilon_{n-1} } a_{ pi_{n} }^{epsilon{n}}, when pi varies over all the permutations in S{n}, and epsilon{i} varies over the set {+1, -1}. By the paper "Hultman Numbers and Generalized Commuting Probability in Finite Groups " (2017), The case where all epsilon{i} are +1 led to a close connection to Hultman numbers. In this paper we generalize the results, permitting epsilon{i} to be -1. We descri…
Balanced-chromatic number and Hadwiger-like conjectures
Universidad de Valparaíso（瓦尔帕莱索大学）；Millennium Nucleus for Social Data Science (SODAS)（社会数据科学千年核（SODAS））；Auburn University（奥本大学）；Université Paris Cité（巴黎西岱大学）；CNRS（法国国家科学研究中心）；IRIF（信息研究与研究所）；École Normale Supérieure, Paris（巴黎高等师范学院）
