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On the Asymptotics of Certain Colored Partitions 关于某些有色分区的渐近性
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-10-08 DOI: 10.1007/s00026-025-00771-0
Lukas Mauth
{"title":"On the Asymptotics of Certain Colored Partitions","authors":"Lukas Mauth","doi":"10.1007/s00026-025-00771-0","DOIUrl":"10.1007/s00026-025-00771-0","url":null,"abstract":"<div><p>We will prove an infinite family of asymptotic formulas for the logarithm of certain two-colored partitions. An infinite sub-family of these asymptotics was posed as a conjecture by Guadalupe.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 1","pages":"251 - 262"},"PeriodicalIF":0.7,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-025-00771-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147558978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Enumeration of Pattern-Avoiding Alternating Sign Matrices: An Asymptotic Dichotomy 避免模式的交替符号矩阵的枚举：一个渐近二分法
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-09-20 DOI: 10.1007/s00026-025-00784-9
Mathilde Bouvel, Eric S. Egge, Rebecca N. Smith, Jessica Striker, Justin M. Troyka
{"title":"Enumeration of Pattern-Avoiding Alternating Sign Matrices: An Asymptotic Dichotomy","authors":"Mathilde Bouvel,&nbsp;Eric S. Egge,&nbsp;Rebecca N. Smith,&nbsp;Jessica Striker,&nbsp;Justin M. Troyka","doi":"10.1007/s00026-025-00784-9","DOIUrl":"10.1007/s00026-025-00784-9","url":null,"abstract":"<div><p>We completely classify the asymptotic behavior of the number of alternating sign matrices classically avoiding a single permutation pattern, in the sense of Johansson and Linusson (Ann Combin 11:471–480, 2007). In particular, we give a uniform proof of an exponential upper bound for the number of alternating sign matrices classically avoiding one of eleven particular patterns, and a super-exponential lower bound for all other single-pattern avoidance classes. We also show that for any fixed integer <i>k</i>, there is an exponential upper bound for the number of alternating sign matrices that classically avoid any single permutation pattern and contain precisely <i>k</i> negative ones. Finally, we prove that there must be at most 3 negative ones in an alternating sign matrix which classically avoids both 2143 and 3412, and we exactly enumerate the number of them with precisely 3 negative ones.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 1","pages":"195 - 225"},"PeriodicalIF":0.7,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560774","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
Extremal Spectral Radius of Outplanar Graphs with Forbidden Structures 具有禁止结构的外平面图的极值谱半径
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-06-28 DOI: 10.1007/s00026-025-00769-8
Wen-Huan Wang, Huan-Lei Shi, Yuan-Zheng-Fang Sun
{"title":"Extremal Spectral Radius of Outplanar Graphs with Forbidden Structures","authors":"Wen-Huan Wang,&nbsp;Huan-Lei Shi,&nbsp;Yuan-Zheng-Fang Sun","doi":"10.1007/s00026-025-00769-8","DOIUrl":"10.1007/s00026-025-00769-8","url":null,"abstract":"<div><p>Among the set of outerplanar graphs on <i>n</i> vertices with a forbidden structure <i>F</i>, we obtain that the extremal graph having the maximum spectral radius contains a subgraph <span>(K_{1,n-1})</span>, where <i>F</i> is an arbitrary graph in a large family of outerplanar graphs with <span>(n geqslant 400)</span>. Based on our new results obtained here, we characterize the unique graph having the maximum spectral radius among the set of outerplanar graphs on <i>n</i> vertices with a forbidden structure <span>(F_1)</span>, where <span>(F_1)</span> is a friendship graph, a given number of independent edges, a fan graph, a cycle, and a generalized theta graph.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 1","pages":"227 - 249"},"PeriodicalIF":0.7,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561793","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
A Trivariate Dichromate Polynomial for Digraphs 有向图的三变量重铬酸盐多项式
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-06-06 DOI: 10.1007/s00026-025-00766-x
Winfried Hochstättler, Johanna Wiehe
{"title":"A Trivariate Dichromate Polynomial for Digraphs","authors":"Winfried Hochstättler,&nbsp;Johanna Wiehe","doi":"10.1007/s00026-025-00766-x","DOIUrl":"10.1007/s00026-025-00766-x","url":null,"abstract":"<div><p>We define a trivariate polynomial combining the NL-coflow and the NL-flow polynomial, which build a dual pair counting acyclic colorings of directed graphs, in the more general setting of regular oriented matroids.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 1","pages":"1 - 16"},"PeriodicalIF":0.7,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-025-00766-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147558950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Induced Saturation of the Poset (2C_2) 波塞特的诱导饱和 (2C_2)
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-05-30 DOI: 10.1007/s00026-025-00764-z
Ryan R. Martin, Nick Veldt
{"title":"Induced Saturation of the Poset (2C_2)","authors":"Ryan R. Martin,&nbsp;Nick Veldt","doi":"10.1007/s00026-025-00764-z","DOIUrl":"10.1007/s00026-025-00764-z","url":null,"abstract":"<div><p>Given a set <i>X</i>, the power set <span>(mathcal {P}(X))</span>, and a finite poset <span>((P,le _P))</span>, a family <span>(mathcal {F}subseteq mathcal {P}(X))</span> is said to be induced-<i>P</i>-free if there is no injection <span>(varphi : Prightarrow mathcal {F})</span> such that <span>(varphi (p)subseteq varphi (q))</span> if and only if <span>(ple _{P} q)</span> for every <span>(p,q in P)</span>. The family <span>(mathcal {F})</span> is <i>induced-P-saturated</i> if it is maximal with respect to being induced-<i>P</i>-free. If <span>(n=|X|)</span>, then the size of the smallest induced-<i>P</i>-saturated family in <span>(mathcal {P}(X))</span> is denoted <span>(textrm{sat}^*(n,P))</span>. The poset <span>(2C_2)</span> is two incomparable 2-chains (the Hasse diagram is two vertex-disjoint edges) and Keszegh, Lemons, Martin, Pálvölgyi, and Patkós proved that <span>(n+2le textrm{sat}^*(n,2C_2)le 2n)</span> and gave one isomorphism class of an induced-<span>(2C_2)</span>-saturated family that achieves the upper bound. We show that the lower bound can be improved to <span>(3n/2 + 1/2)</span> by examining the necessary structure of a saturated family. In addition, we provide many examples of induced-<span>(2C_2)</span>-saturated families of size 2<i>n</i> in <span>(mathcal {P}(X))</span> where <span>(|X|=n)</span>.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 1","pages":"77 - 90"},"PeriodicalIF":0.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147562051","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
Regularity of Powers and Symbolic Powers of Edge Ideals of Cubic Circulant Graphs 三次循环图边理想的幂和符号幂的正则性
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-05-26 DOI: 10.1007/s00026-025-00765-y
Nguyen Thu Hang, My Hanh Pham, Thanh Vu
{"title":"Regularity of Powers and Symbolic Powers of Edge Ideals of Cubic Circulant Graphs","authors":"Nguyen Thu Hang,&nbsp;My Hanh Pham,&nbsp;Thanh Vu","doi":"10.1007/s00026-025-00765-y","DOIUrl":"10.1007/s00026-025-00765-y","url":null,"abstract":"<div><p>We compute the regularity of powers and symbolic powers of edge ideals of all cubic circulant graphs. In particular, we establish Minh’s conjecture for cubic circulant graphs.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 1","pages":"177 - 193"},"PeriodicalIF":0.7,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561340","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
Connected Components and Non-bipartiteness of Generalized Paley Graphs 广义Paley图的连通分量与非二分性
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-05-20 DOI: 10.1007/s00026-025-00758-x
Ricardo A. Podestá, Denis E. Videla
{"title":"Connected Components and Non-bipartiteness of Generalized Paley Graphs","authors":"Ricardo A. Podestá,&nbsp;Denis E. Videla","doi":"10.1007/s00026-025-00758-x","DOIUrl":"10.1007/s00026-025-00758-x","url":null,"abstract":"<div><p>In this work, we consider the class of Cayley graphs known as generalized Paley graphs (GP-graphs for short) given by <span>(Gamma (k,q) = textrm{Cay}({mathbb {F}}_q, {x^k: xin {mathbb {F}}_q^* }))</span>, where <span>({mathbb {F}}_q)</span> is a finite field with <i>q</i> elements, both in the directed and undirected case. Hence <span>(q=p^m)</span> with <i>p</i> prime, <span>(min {mathbb {N}})</span> and one can assume that <span>(kmid q-1)</span>. We first give the connected components of an arbitrary GP-graph. We show that these components are smaller GP-graphs all isomorphic to each other (generalizing Lim and Praeger’s result from 2009 to the directed case). We then characterize those GP-graphs which are disjoint unions of odd cycles. Finally, we show that <span>(Gamma (k,q))</span> is non-bipartite except for the graphs <span>(Gamma (2^{m-1},2^m))</span>, <span>(m in {mathbb {N}})</span>, which are isomorphic to <span>(K_2 sqcup cdots sqcup K_2)</span>, the disjoint union of <span>(2^{m-1})</span> copies of <span>(K_2)</span>.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 4","pages":"1235 - 1259"},"PeriodicalIF":0.7,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145435828","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
Correction to: The Likely Maximum Size of Twin Subtrees in a Large Random Tree 修正：大型随机树中孪生子树的可能最大大小
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-05-17 DOI: 10.1007/s00026-025-00761-2
Miklós Bóna, Ovidiu Costin, Boris Pittel
{"title":"Correction to: The Likely Maximum Size of Twin Subtrees in a Large Random Tree","authors":"Miklós Bóna,&nbsp;Ovidiu Costin,&nbsp;Boris Pittel","doi":"10.1007/s00026-025-00761-2","DOIUrl":"10.1007/s00026-025-00761-2","url":null,"abstract":"","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 3","pages":"945 - 946"},"PeriodicalIF":0.7,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037168","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
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
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