European Journal of Combinatorics最新文献_第5页

Ramsey goodness of k-uniform paths, or the lack thereof k 条均匀路径的拉姆齐性或缺乏拉姆齐性

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-07-01 DOI: 10.1016/j.ejc.2024.104021

Simona Boyadzhiyska, Allan Lo

引用次数: 0

Links in orthoplicial Apollonian packings 正交阿波罗包装中的链接

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-06-28 DOI: 10.1016/j.ejc.2024.104017

Jorge L. Ramírez Alfonsín , Iván Rasskin

引用次数: 0

Asymptotics of local face distributions and the face distribution of the complete graph 局部面分布的渐近性和完整图的面分布

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-06-27 DOI: 10.1016/j.ejc.2024.104019

Jesse Campion Loth

{"title":"Asymptotics of local face distributions and the face distribution of the complete graph","authors":"Jesse Campion Loth","doi":"10.1016/j.ejc.2024.104019","DOIUrl":"https://doi.org/10.1016/j.ejc.2024.104019","url":null,"abstract":"<div>We are interested in the distribution of the number of faces across all the <math><mrow><mn>2</mn><mo>−</mo></mrow></math>cell embeddings of a graph, which is equivalent to the distribution of genus by Euler’s formula. In order to study this distribution, we consider the local distribution of faces at a single vertex. We show an asymptotic uniformity on this local face distribution which holds for any graph with large vertex degrees.We use this to study the usual face distribution of the complete graph. We show that in this case, the local face distribution determines the face distribution for almost all of the whole graph. We use this result to show that a portion of the complete graph of size <math><mrow><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>o</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mo>)</mo></mrow><mrow><mo>|</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>|</mo></mrow></mrow></math> has the same face distribution as the set of all permutations, up to parity. Along the way, we prove new character bounds and an asymptotic uniformity on conjugacy class products.</div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0195669824001045/pdfft?md5=fc1ded09367fd9c944d4c7c3dd000f19&pid=1-s2.0-S0195669824001045-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141479937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Full asymptotic expansion for orbit-summable quadrant walks and discrete polyharmonic functions 轨道可和象限行走和离散多谐函数的完全渐近展开

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-06-27 DOI: 10.1016/j.ejc.2024.104015

Andreas Nessmann

{"title":"Full asymptotic expansion for orbit-summable quadrant walks and discrete polyharmonic functions","authors":"Andreas Nessmann","doi":"10.1016/j.ejc.2024.104015","DOIUrl":"https://doi.org/10.1016/j.ejc.2024.104015","url":null,"abstract":"<div>Enumeration of walks with small steps in the quadrant has been a topic of great interest in combinatorics over the last few years. In this article, it is shown how to compute exact asymptotics of the number of such walks with fixed start- and endpoints for orbit-summable models with finite group, up to arbitrary precision. The resulting representation greatly resembles one conjectured for walks starting from the origin in 2020 by Chapon, Fusy and Raschel, differing only in terms appearing due to the periodicity of the model. We will see that the dependency on start- and endpoint is given by discrete polyharmonic functions, which are solutions of <math><mrow><msup><mrow><mo>△</mo></mrow><mrow><mi>n</mi></mrow></msup><mi>v</mi><mo>=</mo><mn>0</mn></mrow></math> for a discretization <math><mo>△</mo></math> of a Laplace–Beltrami operator. They can be decomposed into a sum of products of lower order polyharmonic functions of either the start- or the endpoint only, which leads to a partial extension of a theorem by Denisov and Wachtel.</div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0195669824001008/pdfft?md5=e67c218ef49f6659d9d12b5f0c3f5a77&pid=1-s2.0-S0195669824001008-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141479936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Two problems on subset sums 关于子集和的两个问题

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-06-22 DOI: 10.1016/j.ejc.2024.104016

Xing-Wang Jiang , Bing-Ling Wu

引用次数: 0

Corrigendum to “Describing quasi-graphic matroids” [European J. Combin. 85 (2020) 103062] 对 "描述准图形矩阵 "的更正 [European J. Combin.

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-06-10 DOI: 10.1016/j.ejc.2024.104004

引用次数: 0

t-sails and sparse hereditary classes of unbounded tree-width 无界树宽的 t 帆和稀疏遗传类

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-06-10 DOI: 10.1016/j.ejc.2024.104005

D. Cocks

{"title":"t-sails and sparse hereditary classes of unbounded tree-width","authors":"D. Cocks","doi":"10.1016/j.ejc.2024.104005","DOIUrl":"https://doi.org/10.1016/j.ejc.2024.104005","url":null,"abstract":"<div>It has long been known that the following basic objects are obstructions to bounded tree-width: for arbitrarily large <math><mi>t</mi></math>, <math><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></math> the complete graph <math><msub><mrow><mi>K</mi></mrow><mrow><mi>t</mi></mrow></msub></math>, <math><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></math> the complete bipartite graph <math><msub><mrow><mi>K</mi></mrow><mrow><mi>t</mi><mo>,</mo><mi>t</mi></mrow></msub></math>, <math><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></math> a subdivision of the <math><mrow><mo>(</mo><mi>t</mi><mo>×</mo><mi>t</mi><mo>)</mo></mrow></math>-wall and <math><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></math> the line graph of a subdivision of the <math><mrow><mo>(</mo><mi>t</mi><mo>×</mo><mi>t</mi><mo>)</mo></mrow></math>-wall. We now add a further boundary object to this list, a <math><mi>t</mi></math>-sail. These results have been obtained by studying sparse hereditary path-star graph classes, each of which consists of the finite induced subgraphs of a single infinite graph whose edges can be partitioned into a path (or forest of paths) with a forest of stars, characterised by an infinite word over a possibly infinite alphabet. We show that a path-star class whose infinite graph has an unbounded number of stars, each of which connects an unbounded number of times to the path, has unbounded tree-width. In addition, we show that such a class is not a subclass of the hereditary class of circle graphs. We identify a collection of nested words with a recursive structure that exhibit interesting characteristics when used to define a path-star graph class. These graph classes do not contain any of the four basic obstructions but instead contain graphs that have large tree-width if and only if they contain arbitrarily large <math><mi>t</mi></math>-sails. We show that these classes are infinitely defined and, like classes of bounded degree or classes excluding a fixed minor, do not contain a minimal class of unbounded tree-width.</div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0195669824000908/pdfft?md5=e4d9091488efe1ad037850e52d6372a3&pid=1-s2.0-S0195669824000908-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141298105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Special Issue dedicated to the memory of Pierre Rosenstiehl 纪念皮埃尔-罗森施蒂尔特刊

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-06-01 DOI: 10.1016/j.ejc.2023.103800

Robert Cori (Editors), Jaroslav Nešetřil, Patrice Ossona de Mendez

引用次数: 0

Permutation Tutte polynomial 置换图特多项式

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-06-01 DOI: 10.1016/j.ejc.2024.104003

Csongor Beke , Gergely Kál Csáji , Péter Csikvári , Sára Pituk

引用次数: 0

Wachs permutations, Bruhat order and weak order 瓦克斯排列、布鲁哈特阶和弱阶

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-06-01 DOI: 10.1016/j.ejc.2023.103804

Francesco Brenti , Paolo Sentinelli

引用次数: 0