Annals of Combinatorics最新文献

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

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, Wenwen Zhang","doi":"10.1007/s00026-025-00748-z","DOIUrl":"10.1007/s00026-025-00748-z","url":null,"abstract":"<div>A graph G is k list equitably colorable, if for any given k-uniform list assignment L, G is L-colorable and each color appears on at most (lceil frac{|V(G)|}{k}rceil ) vertices. Kostochka et al. conjectured that if G is a connected graph with maximum degree at least 3, then G is (Delta (G)) list equitably colorable, unless G is a complete graph or is (K_{k,k}) for some odd k. An equitable k-coloring c of G is a mapping c from V(G) to ([k]={1,2,ldots ,k}) such that (c(u)ne c(v)) for each (uvin E(G)), and for each (k_i), (k_j in [k]), (||{v|c(v)=k_i}|-|{w|c(w)=k_j}||le 1). Chen et al. conjectured that each connected graph with maximum degree (Delta ) that is different from the complete graph (K_{Delta +1}), the complete bipartite graph (K_{Delta , Delta }) and an odd cycle admits an equitable coloring with (Delta ) colors. In this paper, we prove that if G is a planar graph without 5-cycles, then G is k list equitably colorable and equitably k-colorable where (kge max {Delta (G),7}).</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

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

引用次数: 0

Mixing on Generalized Associahedra 广义结合面上的混合

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2025-03-18 DOI: 10.1007/s00026-025-00750-5

William Chang, Colin Defant, Daniel Frishberg

引用次数: 0

Correction to: Positivity Among P-Partition Generating Functions 对p -分区生成函数间正性的修正

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2025-03-14 DOI: 10.1007/s00026-025-00744-3

Nathan R. T. Lesnevich, Peter R. W. McNamara

引用次数: 0

Minimum Quantum Degrees with Maya Diagrams 最小量子度与玛雅图表

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2025-03-06 DOI: 10.1007/s00026-025-00749-y

Ryan M. Shifler

引用次数: 0

Bubble Lattices II: Combinatorics 泡格II：组合学

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2025-02-07 DOI: 10.1007/s00026-025-00743-4

Thomas McConville, Henri Mühle

引用次数: 0

The Connectivity of Friends-and-Strangers Graphs on Complete Multipartite Graphs 完全多部图上朋友与陌生人图的连通性

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2024-12-31 DOI: 10.1007/s00026-024-00740-z

Honglin Zhu

引用次数: 0

Completing the Asymptotic Classification of Mostly Symmetric Short Step Walks in an Orthant 完成正交上大部分对称短步行走的渐近分类

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2024-12-20 DOI: 10.1007/s00026-024-00739-6

Alexander Kroitor, Stephen Melczer

引用次数: 0

Local Limit Theorems for Hook Lengths in Partitions 分区中钩子长度的局部极限定理

IF 0.7 4区数学

Annals of Combinatorics Pub Date : 2024-12-11 DOI: 10.1007/s00026-024-00737-8

Tapas Bhowmik, Wei-Lun Tsai

{"title":"Local Limit Theorems for Hook Lengths in Partitions","authors":"Tapas Bhowmik, Wei-Lun Tsai","doi":"10.1007/s00026-024-00737-8","DOIUrl":"10.1007/s00026-024-00737-8","url":null,"abstract":"<div>Partition hook lengths have wide-ranging applications in combinatorics, number theory, physics, and representation theory. We study two infinite families of random variables associated with t-hooks. For fixed (tge 1,) if (Y_{t;,n}) counts the number of hooks of length t in a random integer partition of n, we prove a uniform local limit theorem for (Y_{t;,n}) on any bounded set of ({mathbb {R}}.) To achieve this, we establish an asymptotic formula with a power-saving error term for the number of partitions of n with m many t-hooks. In contrast, we define ({widehat{Y}}_{t;,n}) as the count of hooks divisible by t in a randomly chosen partition of n. While ({widehat{Y}}_{t;,n}) converges in distribution, we show that it fails to satisfy the local limit theorem for any (t ge 2). The proofs employ the multivariable saddle-point method, asymptotic formulas for the number of t-core partitions from Anderson and Lulov–Pittel, and estimates of certain exponential sums. Notably, for (t=4,) the analysis involves the asymptotic behavior of class numbers of imaginary quadratic fields.</div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 3","pages":"853 - 884"},"PeriodicalIF":0.7,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-024-00737-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037274","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