可定向顶点原始完整映射

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Annals of Combinatorics Pub Date : 2024-10-07 DOI:10.1007/s00026-024-00721-2

Xue Yu, Cai Heng Li, Ben Gong Lou

{"title":"可定向顶点原始完整映射","authors":"Xue Yu, Cai Heng Li, Ben Gong Lou","doi":"10.1007/s00026-024-00721-2","DOIUrl":null,"url":null,"abstract":"<div><p>An orientable vertex primitive complete map is a two-cell embedding of a complete graph into an orientable surface such that the automorphism group of this map acts primitively on its vertex set. The paper is devoted to the problem of enumerating orientable vertex primitive complete maps. For a given integer <i>n</i>, we derive the number of different such maps with <i>n</i> vertices. Furthermore, we obtain explicit formulas for the numbers of non-isomorphic orientable vertex primitive complete maps with <i>n</i> vertices.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"28 4","pages":"1127 - 1139"},"PeriodicalIF":0.6000,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Orientable Vertex Primitive Complete Maps\",\"authors\":\"Xue Yu, Cai Heng Li, Ben Gong Lou\",\"doi\":\"10.1007/s00026-024-00721-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>An orientable vertex primitive complete map is a two-cell embedding of a complete graph into an orientable surface such that the automorphism group of this map acts primitively on its vertex set. The paper is devoted to the problem of enumerating orientable vertex primitive complete maps. For a given integer <i>n</i>, we derive the number of different such maps with <i>n</i> vertices. Furthermore, we obtain explicit formulas for the numbers of non-isomorphic orientable vertex primitive complete maps with <i>n</i> vertices.</p></div>\",\"PeriodicalId\":50769,\"journal\":{\"name\":\"Annals of Combinatorics\",\"volume\":\"28 4\",\"pages\":\"1127 - 1139\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-10-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Combinatorics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00026-024-00721-2\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00026-024-00721-2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

可定向顶点原始完整映射是将完整图嵌入可定向曲面的双胞嵌入，使得该映射的自变群原始地作用于其顶点集。本文主要研究枚举可定向顶点原始完整映射的问题。对于给定的整数 n，我们推导出具有 n 个顶点的不同此类映射的数量。此外，我们还得到了具有 n 个顶点的非同构可定向顶点原始完整映射的数量的明确公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Orientable Vertex Primitive Complete Maps

查看原文本刊更多论文

Orientable Vertex Primitive Complete Maps

An orientable vertex primitive complete map is a two-cell embedding of a complete graph into an orientable surface such that the automorphism group of this map acts primitively on its vertex set. The paper is devoted to the problem of enumerating orientable vertex primitive complete maps. For a given integer n, we derive the number of different such maps with n vertices. Furthermore, we obtain explicit formulas for the numbers of non-isomorphic orientable vertex primitive complete maps with n vertices.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Annals of Combinatorics 数学-应用数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annals of Combinatorics publishes outstanding contributions to combinatorics with a particular focus on algebraic and analytic combinatorics, as well as the areas of graph and matroid theory. Special regard will be given to new developments and topics of current interest to the community represented by our editorial board. The scope of Annals of Combinatorics is covered by the following three tracks: Algebraic Combinatorics: Enumerative combinatorics, symmetric functions, Schubert calculus / Combinatorial Hopf algebras, cluster algebras, Lie algebras, root systems, Coxeter groups / Discrete geometry, tropical geometry / Discrete dynamical systems / Posets and lattices Analytic and Algorithmic Combinatorics: Asymptotic analysis of counting sequences / Bijective combinatorics / Univariate and multivariable singularity analysis / Combinatorics and differential equations / Resolution of hard combinatorial problems by making essential use of computers / Advanced methods for evaluating counting sequences or combinatorial constants / Complexity and decidability aspects of combinatorial sequences / Combinatorial aspects of the analysis of algorithms Graphs and Matroids: Structural graph theory, graph minors, graph sparsity, decompositions and colorings / Planar graphs and topological graph theory, geometric representations of graphs / Directed graphs, posets / Metric graph theory / Spectral and algebraic graph theory / Random graphs, extremal graph theory / Matroids, oriented matroids, matroid minors / Algorithmic approaches