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Self-Reachable Configuration Polytopes for Trees 树的自可达配置多边形
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-05-15 DOI: 10.1007/s00026-025-00763-0
Benjamin Lyons, McCabe Olsen
{"title":"Self-Reachable Configuration Polytopes for Trees","authors":"Benjamin Lyons,&nbsp;McCabe Olsen","doi":"10.1007/s00026-025-00763-0","DOIUrl":"10.1007/s00026-025-00763-0","url":null,"abstract":"<div><p>We study lattice polytopes which arise as the convex hull of chip vectors for <i>self-reachable</i> chip configurations on a tree <i>T</i>. We show that these polytopes always have the integer decomposition property and characterize the vertex sets of these polytopes. Additionally, in the case of self-reachable configurations with the smallest possible number of chips, we show that these polytopes are unimodularly equivalent to a unit cube.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 1","pages":"131 - 154"},"PeriodicalIF":0.7,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Periods and Atomic Firing Sequences of Parallel Chip-Firing Games on Directed Graphs 有向图上并行芯片发射游戏的周期和原子发射序列
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-05-13 DOI: 10.1007/s00026-025-00760-3
David Ji, Michael Li, Daniel Wang
{"title":"Periods and Atomic Firing Sequences of Parallel Chip-Firing Games on Directed Graphs","authors":"David Ji,&nbsp;Michael Li,&nbsp;Daniel Wang","doi":"10.1007/s00026-025-00760-3","DOIUrl":"10.1007/s00026-025-00760-3","url":null,"abstract":"<div><p>In 1992, Bitar and Goles introduced the parallel chip-firing game on undirected graphs. Two years later, Prisner extended the game to directed graphs. While the properties of parallel chip-firing games on undirected graphs have been extensively studied, their analogs for parallel chip-firing games on directed graphs have been sporadic. In this paper, we prove the outstanding analogs of the core results of parallel chip-firing games on undirected graphs for those on directed graphs. We find the possible periods of a parallel chip-firing game on a directed simple cycle and introduce the method of Gauss–Jordan elimination on a Laplacian-like matrix to establish a lower bound on the maximum period of a parallel chip-firing game on an orientation of an undirected complete graph and an undirected complete bipartite graph. Finally, we expand the method of motors by Jiang, Scully, and Zhang to directed graphs to show that a binary string <i>s</i> can be the atomic firing sequence of a vertex in a parallel chip-firing game on a strongly connected directed graph if and only if <i>s</i> contains 1 or <span>(s=0)</span>.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 4","pages":"1155 - 1175"},"PeriodicalIF":0.7,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145435864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Zeta Functions of Geometrically Finite Graphs of Groups 几何有限群图的Zeta函数
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-05-07 DOI: 10.1007/s00026-025-00759-w
Soonki Hong, Sanghoon Kwon
{"title":"Zeta Functions of Geometrically Finite Graphs of Groups","authors":"Soonki Hong,&nbsp;Sanghoon Kwon","doi":"10.1007/s00026-025-00759-w","DOIUrl":"10.1007/s00026-025-00759-w","url":null,"abstract":"<div><p>In this paper, we explore the properties of zeta functions associated with infinite graphs of groups that arise as quotients of cuspidal tree lattices, including all non-uniform arithmetic quotients of the tree of rank-one Lie groups over local fields. Through various examples, we illustrate pairs of non-isomorphic cuspidal tree lattices with the same Ihara zeta function. In addition, we analyze the spectral behavior of a sequence of graphs of groups whose pole-free regions of zeta functions converge towards 0, which also presents an example of arbitrary small exponential error term in counting geodesic formula.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 4","pages":"995 - 1018"},"PeriodicalIF":0.7,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145435829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Equitable and List Equitable Colorings of Planar Graphs Without 5-Cycles 无5环平面图的公平着色与列表公平着色
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-04-30 DOI: 10.1007/s00026-025-00748-z
Aijun Dong, Wenwen Zhang
{"title":"Equitable and List Equitable Colorings of Planar Graphs Without 5-Cycles","authors":"Aijun Dong,&nbsp;Wenwen Zhang","doi":"10.1007/s00026-025-00748-z","DOIUrl":"10.1007/s00026-025-00748-z","url":null,"abstract":"<div><p>A graph <i>G</i> is <i>k</i> list equitably colorable, if for any given <i>k</i>-uniform list assignment <i>L</i>, <i>G</i> is <i>L</i>-colorable and each color appears on at most <span>(lceil frac{|V(G)|}{k}rceil )</span> vertices. Kostochka et al. conjectured that if <i>G</i> is a connected graph with maximum degree at least 3, then <i>G</i> is <span>(Delta (G))</span> list equitably colorable, unless <i>G</i> is a complete graph or is <span>(K_{k,k})</span> for some odd <i>k</i>. An equitable <i>k</i>-coloring <i>c</i> of <i>G</i> is a mapping <i>c</i> from <i>V</i>(<i>G</i>) to <span>([k]={1,2,ldots ,k})</span> such that <span>(c(u)ne c(v))</span> for each <span>(uvin E(G))</span>, and for each <span>(k_i)</span>, <span>(k_j in [k])</span>, <span>(||{v|c(v)=k_i}|-|{w|c(w)=k_j}||le 1)</span>. Chen et al. conjectured that each connected graph with maximum degree <span>(Delta )</span> that is different from the complete graph <span>(K_{Delta +1})</span>, the complete bipartite graph <span>(K_{Delta , Delta })</span> and an odd cycle admits an equitable coloring with <span>(Delta )</span> colors. In this paper, we prove that if <i>G</i> is a planar graph without 5-cycles, then <i>G</i> is <i>k</i> list equitably colorable and equitably <i>k</i>-colorable where <span>(kge max {Delta (G),7})</span>.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 3","pages":"637 - 656"},"PeriodicalIF":0.7,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Moments of Colored Permutation Statistics on Conjugacy Classes 共轭类上有色置换统计量的矩
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-04-21 DOI: 10.1007/s00026-025-00757-y
Jesse Campion Loth, Michael Levet, Kevin Liu, Sheila Sundaram, Mei Yin
{"title":"Moments of Colored Permutation Statistics on Conjugacy Classes","authors":"Jesse Campion Loth,&nbsp;Michael Levet,&nbsp;Kevin Liu,&nbsp;Sheila Sundaram,&nbsp;Mei Yin","doi":"10.1007/s00026-025-00757-y","DOIUrl":"10.1007/s00026-025-00757-y","url":null,"abstract":"<div><p>In this paper, we consider the moments of statistics on conjugacy classes of the colored permutation groups <span>({mathfrak {S}}_{n,r}=mathbb {Z}_rwr {mathfrak {S}}_n)</span>. We first show that any fixed moment of a statistic coincides on all conjugacy classes where all cycles have sufficiently long length. Additionally, for permutation statistics that can be realized via a process we call order-invariant extension, these moments are polynomials in <i>n</i>. Finally, for the descent statistic on the hyperoctahedral group <span>(B_ncong {mathfrak {S}}_{n,2})</span>, we show that its distribution on conjugacy classes without short cycles satisfies a central limit theorem. Our results build on and generalize previous work of Fulman (J Comb Theory Ser A, 1998), Hamaker and Rhoades (arXiv, 2022), and Campion Loth et al. (arXiv, 2023). In particular, our techniques utilize the latter combinatorial framework.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 4","pages":"1109 - 1153"},"PeriodicalIF":0.7,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145435940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
One-element Extensions of Hyperplane Arrangements 超平面排列的单元素扩展
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-04-12 DOI: 10.1007/s00026-025-00756-z
Hang Cai, Houshan Fu, Suijie Wang
{"title":"One-element Extensions of Hyperplane Arrangements","authors":"Hang Cai,&nbsp;Houshan Fu,&nbsp;Suijie Wang","doi":"10.1007/s00026-025-00756-z","DOIUrl":"10.1007/s00026-025-00756-z","url":null,"abstract":"<div><p>Let <span>({mathcal {A}})</span> be a hyperplane arrangement in the <i>d</i>-dimensional vector space <span>({mathbb {F}}^d)</span>. We study one-element extensions <span>({mathcal {A}}+H_{varvec{alpha },a})</span> of <span>({mathcal {A}})</span> for all <span>((varvec{alpha },a)in {mathbb {F}}^{d+1})</span>. Their intersection semi-lattices <span>(L({mathcal {A}}+H_{varvec{alpha },a}))</span> and other combinatorial invariants, including Whitney polynomials, characteristic polynomials, Whitney numbers and face numbers, can be classified by the intersection lattice of the induced adjoint arrangement of <span>({mathcal {A}})</span>. As a byproduct, we further establish order-preserving relations on these combinatorial invariants and obtain a decomposition formula for the characteristic polynomials <span>(chi ({mathcal {A}}+H_{varvec{alpha },a},t))</span>.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 4","pages":"955 - 978"},"PeriodicalIF":0.7,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145435936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Perfect Matching Complexes of Polygonal Line Tilings 多边形线条平铺的完美匹配复合体
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-04-05 DOI: 10.1007/s00026-025-00755-0
Himanshu Chandrakar, Anurag Singh
{"title":"Perfect Matching Complexes of Polygonal Line Tilings","authors":"Himanshu Chandrakar,&nbsp;Anurag Singh","doi":"10.1007/s00026-025-00755-0","DOIUrl":"10.1007/s00026-025-00755-0","url":null,"abstract":"<div><p>The <i>perfect matching complex</i> of a simple graph <i>G</i> is a simplicial complex having facets (maximal faces) as the <i>perfect matchings</i> of <i>G</i>. This article discusses the perfect matching complex of polygonal line tilings and the <span>(left( 2 times nright) )</span>-grid graph in particular. We use tools from discrete Morse theory to show that the perfect matching complex of any polygonal line tiling is either contractible or homotopy equivalent to a wedge of spheres. While proving our results, we also characterize all the matchings of <span>(left( 2 times nright) )</span>-grid graph that cannot be extended to form a perfect matching.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 4","pages":"1211 - 1233"},"PeriodicalIF":0.7,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145435938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Genus Polynomials of Cubic Graphs with Non-real Roots 非实根三次图的属多项式
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-04-03 DOI: 10.1007/s00026-025-00754-1
MacKenzie Carr, Varpreet Dhaliwal, Bojan Mohar
{"title":"Genus Polynomials of Cubic Graphs with Non-real Roots","authors":"MacKenzie Carr,&nbsp;Varpreet Dhaliwal,&nbsp;Bojan Mohar","doi":"10.1007/s00026-025-00754-1","DOIUrl":"10.1007/s00026-025-00754-1","url":null,"abstract":"<div><p>Given a graph <i>G</i>, its genus polynomial is <span>(Gamma _G(x) = sum _{kge 0} g_k(G)x^k)</span>, where <span>(g_k(G))</span> is the number of two-cell embeddings of <i>G</i> in an orientable surface of genus <i>k</i>. The Log-Concavity Genus Distribution (LCGD) Conjecture states that the genus polynomial of every graph is log-concave. It was further conjectured by Stahl that the genus polynomial of every graph has only real roots, however, this was later disproved. We identify several examples of cubic graphs whose genus polynomials, in addition to having at least one non-real root, have a quadratic factor that is non-log-concave when factored over the real numbers.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 3","pages":"885 - 892"},"PeriodicalIF":0.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Increasing Binary Trees and the ((alpha ,beta ))-Eulerian Polynomials 递增二叉树和((alpha ,beta )) -欧拉多项式
IF 0.8 4区 数学
Annals of Combinatorics Pub Date : 2025-03-28 DOI: 10.1007/s00026-025-00752-3
William Y. C. Chen, Amy M. Fu
{"title":"Increasing Binary Trees and the ((alpha ,beta ))-Eulerian Polynomials","authors":"William Y. C. Chen,&nbsp;Amy M. Fu","doi":"10.1007/s00026-025-00752-3","DOIUrl":"10.1007/s00026-025-00752-3","url":null,"abstract":"<div><p>In light of the grammar given by Ji for the <span>((alpha ,beta ))</span>-Eulerian polynomials introduced by Carlitz and Scoville, we provide a labeling scheme for increasing binary trees. In this setting, we obtain a combinatorial interpretation of the <span>(gamma )</span>-coefficients of the <span>(alpha )</span>-Eulerian polynomials in terms of forests of planted 0-1-2-plane trees, which specializes to a combinatorial interpretation of the <span>(gamma )</span>-coefficients of the derangement polynomials in the same spirit. By means of a decomposition of an increasing binary tree into a forest, we find combinatorial interpretations of the sums involving two identities of Ji, one of which can be viewed as <span>((alpha ,beta ))</span>-extensions of the formulas of Petersen and Stembridge.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 2","pages":"263 - 275"},"PeriodicalIF":0.8,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stirling Numbers for Complex Reflection Groups 复反射群的Stirling数
IF 0.8 4区 数学
Annals of Combinatorics Pub Date : 2025-03-24 DOI: 10.1007/s00026-025-00751-4
Bruce E. Sagan, Joshua P. Swanson
{"title":"Stirling Numbers for Complex Reflection Groups","authors":"Bruce E. Sagan,&nbsp;Joshua P. Swanson","doi":"10.1007/s00026-025-00751-4","DOIUrl":"10.1007/s00026-025-00751-4","url":null,"abstract":"<div><p>In an earlier paper, we defined and studied <i>q</i>-analogs of the Stirling numbers of both types for the Coxeter group of type <i>B</i>. In the present work, we show how this approach can be extended to all irreducible complex reflection groups <i>G</i>. The Stirling numbers of the first and second kind are defined via the Whitney numbers of the first and second kind, respectively, of the intersection lattice of <i>G</i>. For the groups <i>G</i>(<i>m</i>, <i>p</i>, <i>n</i>), these numbers and polynomials can be given combinatorial interpretations in terms of various statistics. The ordered version of the <i>q</i>-Stirling numbers of the second kind also show up in conjectured Hilbert series for certain super coinvariant algebras.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 2","pages":"365 - 395"},"PeriodicalIF":0.8,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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