A Simple Proof of the Nonuniform Kahn–Kalai Conjecture

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-07-04 DOI:10.1137/23m1587075

Bryan Park, Jan Vondrák

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2089-2094, September 2024.
Abstract. We revisit the Kahn–Kalai conjecture, recently proved in striking fashion by Park and Pham, and present a slightly reformulated simple proof which has a few advantages: (1) it works for nonuniform product measures, (2) it gives near-optimal bounds even for sampling probabilities close to 1, (3) it gives a clean bound of [math] for every [math]-bounded set system, [math].

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非均匀卡恩-卡莱猜想的简单证明

SIAM 离散数学杂志》，第 38 卷第 3 期，第 2089-2094 页，2024 年 9 月。摘要。我们重温了最近由 Park 和 Pham 以惊人的方式证明的 Kahn-Kalai 猜想，并提出了一个略微重新表述的简单证明，它有几个优点：(1) 它适用于非均匀积度量；(2) 即使在抽样概率接近 1 的情况下，它也给出了接近最优的约束；(3) 它为每一个[math]有界集合系统给出了一个干净的[math]约束[math]。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.