随机超图中的阿贝尔群

IF 0.9 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Combinatorics, Probability & Computing Pub Date : 2023-04-20 DOI:10.1017/s0963548323000056

Andrew Newman

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引用次数: 0

摘要

摘要对于顶点集$\{1, \ldots, n\}$上的一个$k$ -一致超图$\mathcal{H}$，我们在整数上关联了一个特殊的有符号关联矩阵$M(\mathcal{H})$。对于$\mathcal{H} \sim \mathcal{H}_k(n, p)$和Erdős-Rényi随机$k$ -均匀超图，${\mathrm{coker}}(M(\mathcal{H}))$是随机阿贝尔群的模型。从随机简单复合体的研究推测的动机，我们表明，对于$p = \omega (1/n^{k - 1})$, ${\mathrm{coker}}(M(\mathcal{H}))$是无扭转。

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Abelian groups from random hypergraphs

Abstract For a $k$ -uniform hypergraph $\mathcal{H}$ on vertex set $\{1, \ldots, n\}$ we associate a particular signed incidence matrix $M(\mathcal{H})$ over the integers. For $\mathcal{H} \sim \mathcal{H}_k(n, p)$ an Erdős–Rényi random $k$ -uniform hypergraph, ${\mathrm{coker}}(M(\mathcal{H}))$ is then a model for random abelian groups. Motivated by conjectures from the study of random simplicial complexes we show that for $p = \omega (1/n^{k - 1})$ , ${\mathrm{coker}}(M(\mathcal{H}))$ is torsion-free.

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来源期刊

Combinatorics, Probability & Computing 数学-计算机：理论方法

CiteScore

2.40

自引率

11.10%

发文量

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.