European Journal of Combinatorics最新文献_第4页

Non-geometric distance-regular graphs of diameter at least 3 with smallest eigenvalue at least −3 直径至少为3且最小特征值至少为- 3的非几何距离正则图

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2025-01-18 DOI: 10.1016/j.ejc.2024.104118

Jack H. Koolen , Kefan Yu , Xiaoye Liang , Harrison Choi , Greg Markowsky

引用次数: 0

Visible lattice points in Pólya’s walks 在Pólya的行走中可见的点阵点

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2025-01-16 DOI: 10.1016/j.ejc.2024.104116

Meijie Lu , Xianchang Meng

引用次数: 0

On naturally labelled posets and permutations avoiding 12–34 在自然标记的偏序集和排列上避免12-34

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2025-01-13 DOI: 10.1016/j.ejc.2024.104117

David Bevan , Gi-Sang Cheon , Sergey Kitaev

引用次数: 0

On the maximum number of common neighbours in dense random regular graphs 稠密随机正则图中共同近邻的最大数目

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-12-31 DOI: 10.1016/j.ejc.2024.104106

Mikhail Isaev , Maksim Zhukovskii

引用次数: 0

On heroes in digraphs with forbidden induced forests 论禁止诱导森林的有向图英雄

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-12-26 DOI: 10.1016/j.ejc.2024.104104

Alvaro Carbonero , Hidde Koerts , Benjamin Moore , Sophie Spirkl

{"title":"On heroes in digraphs with forbidden induced forests","authors":"Alvaro Carbonero , Hidde Koerts , Benjamin Moore , Sophie Spirkl","doi":"10.1016/j.ejc.2024.104104","DOIUrl":"10.1016/j.ejc.2024.104104","url":null,"abstract":"<div><div>We continue a line of research which studies which hereditary families of digraphs have bounded dichromatic number. For a class of digraphs <math><mi>C</mi></math>, a hero in <math><mi>C</mi></math> is any digraph <math><mi>H</mi></math> such that <math><mi>H</mi></math>-free digraphs in <math><mi>C</mi></math> have bounded dichromatic number. We show that if <math><mi>F</mi></math> is an oriented star of degree at least five, the only heroes for the class of <math><mi>F</mi></math>-free digraphs are transitive tournaments. For oriented stars <math><mi>F</mi></math> of degree exactly four, we show the only heroes in <math><mi>F</mi></math>-free digraphs are transitive tournaments, or possibly special joins of transitive tournaments. Aboulker et al. characterized the set of heroes of <math><mrow><mo>{</mo><mi>H</mi><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><mover><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mo>→</mo></mover><mo>}</mo></mrow></math>-free digraphs almost completely, and we show the same characterization for the class of <math><mrow><mo>{</mo><mi>H</mi><mo>,</mo><mi>r</mi><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><mover><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow><mo>→</mo></mover><mo>}</mo></mrow></math>-free digraphs. Lastly, we show that if we forbid two “valid” orientations of brooms, then every transitive tournament is a hero for this class of digraphs.</div></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":"125 ","pages":"Article 104104"},"PeriodicalIF":1.0,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136075","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

A group action on cyclic compositions and γ-positivity 环组成与γ-正性的群作用

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-12-20 DOI: 10.1016/j.ejc.2024.104107

Shishuo Fu , Jie Yang

{"title":"A group action on cyclic compositions and γ-positivity","authors":"Shishuo Fu , Jie Yang","doi":"10.1016/j.ejc.2024.104107","DOIUrl":"10.1016/j.ejc.2024.104107","url":null,"abstract":"<div><div>Let <math><msub><mrow><mi>w</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>m</mi></mrow></msub></math> be the number of Dyck paths of semilength <math><mi>n</mi></math> with <math><mi>k</mi></math> occurrences of <math><mrow><mi>U</mi><mi>D</mi></mrow></math> and <math><mi>m</mi></math> occurrences of <math><mrow><mi>U</mi><mi>U</mi><mi>D</mi></mrow></math>. We establish in two ways a new interpretation of the numbers <math><msub><mrow><mi>w</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>m</mi></mrow></msub></math> in terms of plane trees and internal nodes. The first way builds on a new characterization of plane trees that involves cyclic compositions. The second proof utilizes a known interpretation of <math><msub><mrow><mi>w</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>m</mi></mrow></msub></math> in terms of plane trees and leaves, and a recent involution on plane trees constructed by Li, Lin, and Zhao. Moreover, a group action on the set of cyclic compositions (or equivalently, 2-dominant compositions) is introduced, which amounts to give a combinatorial proof of the <math><mi>γ</mi></math>-positivity of the Narayana polynomial, as well as the <math><mi>γ</mi></math>-positivity of the polynomial <math><mrow><msub><mrow><mi>W</mi></mrow><mrow><mn>2</mn><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>≔</mo><msub><mrow><mo>∑</mo></mrow><mrow><mn>1</mn><mo>≤</mo><mi>m</mi><mo>≤</mo><mi>k</mi></mrow></msub><msub><mrow><mi>w</mi></mrow><mrow><mn>2</mn><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>k</mi><mo>,</mo><mi>m</mi></mrow></msub><msup><mrow><mi>t</mi></mrow><mrow><mi>m</mi></mrow></msup></mrow></math> previously obtained by Bóna et al, with apparently new combinatorial interpretations of their <math><mi>γ</mi></math>-coefficients.</div></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":"125 ","pages":"Article 104107"},"PeriodicalIF":1.0,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Coloring minimal Cayley graphs 最小Cayley图的着色

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-12-19 DOI: 10.1016/j.ejc.2024.104108

Ignacio García-Marco , Kolja Knauer

引用次数: 0

Progressions in Euclidean Ramsey theory 欧几里得拉姆齐理论的进展

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-12-13 DOI: 10.1016/j.ejc.2024.104105

Jakob Führer , Géza Tóth

引用次数: 0

Repeatedly applying the Combinatorial Nullstellensatz for Zero-sum Grids to Martin Gardner’s minimum no-3-in-a-line problem 将零和网格的组合nullstellensz反复应用于Martin Gardner的最小3-in- line问题

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-12-12 DOI: 10.1016/j.ejc.2024.104095

Seunghwan Oh , John R. Schmitt , Xianzhi Wang

{"title":"Repeatedly applying the Combinatorial Nullstellensatz for Zero-sum Grids to Martin Gardner’s minimum no-3-in-a-line problem","authors":"Seunghwan Oh , John R. Schmitt , Xianzhi Wang","doi":"10.1016/j.ejc.2024.104095","DOIUrl":"10.1016/j.ejc.2024.104095","url":null,"abstract":"<div><div>A 1976 question of Martin Gardner asks for the minimum size of a placement of queens on an <math><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></math> chessboard that is maximal with respect to the property of ‘no-3-in-a-line’. The work of Cooper, Pikhurko, Schmitt and Warrington showed that this number is at least <math><mi>n</mi></math> in the cases that <math><mrow><mi>n</mi><mo>⁄</mo><mo>≡</mo><mn>3</mn><mspace></mspace><mrow><mo>(</mo><mo>mod</mo><mspace></mspace><mn>4</mn><mo>)</mo></mrow></mrow></math>, and at least <math><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></math> in the case that <math><mrow><mi>n</mi><mo>≡</mo><mn>3</mn><mspace></mspace><mrow><mo>(</mo><mo>mod</mo><mspace></mspace><mn>4</mn><mo>)</mo></mrow></mrow></math>. When <math><mrow><mi>n</mi><mo>></mo><mn>1</mn></mrow></math> is odd, Gardner conjectured the lower bound to be <math><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></math>. We prove this conjecture in the case that <math><mrow><mi>n</mi><mo>≡</mo><mn>1</mn><mspace></mspace><mrow><mo>(</mo><mo>mod</mo><mspace></mspace><mn>4</mn><mo>)</mo></mrow></mrow></math>. The proof relies heavily on a recent advancement to the Combinatorial Nullstellensatz for zero-sum grids due to Bogdan Nica.</div></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":"125 ","pages":"Article 104095"},"PeriodicalIF":1.0,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Classification of countable 2-colored ultrahomogeneous graphs where each color class forms a disjoint union of cliques 可计数2色超齐次图的分类，其中每个色类形成团的不相交并

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2024-12-06 DOI: 10.1016/j.ejc.2024.104093

Sofia Brenner, Irene Heinrich

引用次数: 0