超图的度序列渐近枚举

Q2 Mathematics

Advances in Combinatorics Pub Date : 2020-08-18 DOI:10.19086/aic.32357

Nina Kamvcev, Anita Liebenau, N. Wormald

{"title":"超图的度序列渐近枚举","authors":"Nina Kamvcev, Anita Liebenau, N. Wormald","doi":"10.19086/aic.32357","DOIUrl":null,"url":null,"abstract":"We prove an asymptotic formula for the number of k-uniform hypergraphs with\na given degree sequence, for a wide range of parameters. In particular, we find a formula\nthat is asymptotically equal to the number of d-regular k-uniform hypergraphs on n vertices provided that dn ≤ c(n/k) for a constant c > 0, and 3 ≤ k < n^c for any C < 1/9. Our results relate the degree sequence of a random k-uniform hypergraph to a simple model of nearly independent binomial random variables, thus extending the recent results for graphs due to the second and third author.","PeriodicalId":36338,"journal":{"name":"Advances in Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Asymptotic Enumeration of Hypergraphs by Degree Sequence\",\"authors\":\"Nina Kamvcev, Anita Liebenau, N. Wormald\",\"doi\":\"10.19086/aic.32357\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove an asymptotic formula for the number of k-uniform hypergraphs with\\na given degree sequence, for a wide range of parameters. In particular, we find a formula\\nthat is asymptotically equal to the number of d-regular k-uniform hypergraphs on n vertices provided that dn ≤ c(n/k) for a constant c > 0, and 3 ≤ k < n^c for any C < 1/9. Our results relate the degree sequence of a random k-uniform hypergraph to a simple model of nearly independent binomial random variables, thus extending the recent results for graphs due to the second and third author.\",\"PeriodicalId\":36338,\"journal\":{\"name\":\"Advances in Combinatorics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-08-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.19086/aic.32357\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.19086/aic.32357","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 1

摘要

我们证明了一个关于给定阶序列的k-一致超图数目的渐近公式。特别地，我们发现了一个公式，它渐近地等于n个顶点上的d-正则k-一致超图的个数，条件是对于常数c > 0, dn≤c(n/k)，对于任意c < 1/9, 3≤k < n^c。我们的结果将随机k-均匀超图的度序列与一个几乎独立的二项随机变量的简单模型联系起来，从而扩展了第二和第三作者最近关于图的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Asymptotic Enumeration of Hypergraphs by Degree Sequence

We prove an asymptotic formula for the number of k-uniform hypergraphs with a given degree sequence, for a wide range of parameters. In particular, we find a formula that is asymptotically equal to the number of d-regular k-uniform hypergraphs on n vertices provided that dn ≤ c(n/k) for a constant c > 0, and 3 ≤ k < n^c for any C < 1/9. Our results relate the degree sequence of a random k-uniform hypergraph to a simple model of nearly independent binomial random variables, thus extending the recent results for graphs due to the second and third author.

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

Advances in Combinatorics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

3.10

自引率

0.00%

发文量