Degree sequences of sufficiently dense random uniform hypergraphs

IF 0.9 4区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS
Catherine S. Greenhill, M. Isaev, Tamás Makai, B. McKay
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引用次数: 0

Abstract

We find an asymptotic enumeration formula for the number of simple $r$ -uniform hypergraphs with a given degree sequence, when the number of edges is sufficiently large. The formula is given in terms of the solution of a system of equations. We give sufficient conditions on the degree sequence which guarantee existence of a solution to this system. Furthermore, we solve the system and give an explicit asymptotic formula when the degree sequence is close to regular. This allows us to establish several properties of the degree sequence of a random $r$ -uniform hypergraph with a given number of edges. More specifically, we compare the degree sequence of a random $r$ -uniform hypergraph with a given number edges to certain models involving sequences of binomial or hypergeometric random variables conditioned on their sum.
充分密集随机一致超图的度序列
当边的数目足够大时,我们得到了具有给定阶序列的简单$r$ -一致超图数目的渐近枚举公式。这个公式是以方程组的解的形式给出的。给出了该系统解存在的充分条件。进一步,我们对该系统进行了求解,并给出了当阶序列接近正则时的显式渐近公式。这允许我们建立具有给定边数的随机$r$均匀超图的度序列的几个性质。更具体地说,我们将具有给定数目边的随机$r$ -均匀超图的度序列与涉及二项式或超几何随机变量序列的某些模型进行比较。
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来源期刊
Combinatorics, Probability & Computing
Combinatorics, Probability & Computing 数学-计算机:理论方法
CiteScore
2.40
自引率
11.10%
发文量
33
审稿时长
6-12 weeks
期刊介绍: Published bimonthly, Combinatorics, Probability & Computing is devoted to the three areas of combinatorics, probability theory and theoretical computer science. Topics covered include classical and algebraic graph theory, extremal set theory, matroid theory, probabilistic methods and random combinatorial structures; combinatorial probability and limit theorems for random combinatorial structures; the theory of algorithms (including complexity theory), randomised algorithms, probabilistic analysis of algorithms, computational learning theory and optimisation.
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