随机二维行列式超树的模2同调的界

IF 1 2区数学 Q1 MATHEMATICS

Combinatorica Pub Date : 2025-03-14 DOI:10.1007/s00493-025-00142-6

András Mészáros

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引用次数: 0

摘要

作为Kahle和Newman猜想的第一步，我们证明了如果$T_n$是n个顶点上的随机二维行列式超树，那么$$\begin{aligned} \frac{\dim H_1(T_n,\mathbb {F}_2)}{n^2} \end{aligned}$$在概率上收敛为零。我们证实了Linial和Peled的一个猜想，并证明了1-out - 2络合物的类似命题。我们的证明依赖于Chatterjee和Varadhan的Erdős-Rényi随机图的大偏差原理。

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Bounds on the Mod 2 Homology of Random 2-Dimensional Determinantal Hypertrees

As a first step towards a conjecture of Kahle and Newman, we prove that if $T_n$ is a random 2-dimensional determinantal hypertree on n vertices, then

$$\begin{aligned} \frac{\dim H_1(T_n,\mathbb {F}_2)}{n^2} \end{aligned}$$

converges to zero in probability. Confirming a conjecture of Linial and Peled, we also prove the analogous statement for the 1-out 2-complex. Our proof relies on the large deviation principle for the Erdős–Rényi random graph by Chatterjee and Varadhan.

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来源期刊

Combinatorica 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are - Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups). - Combinatorial optimization. - Combinatorial aspects of geometry and number theory. - Algorithms in combinatorics and related fields. - Computational complexity theory. - Randomization and explicit construction in combinatorics and algorithms.