一个有效容器引理

IF 1 3区数学 Q1 MATHEMATICS

Discrete Analysis Pub Date : 2019-10-21 DOI:10.19086/DA.17354

J. Balogh, W. Samotij

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引用次数: 11

摘要

我们证明了超图容器定理的一个新的、有效的版本，它适用于具有大一致性的超图。主要的新颖性是一种构建容器的精细方法，该方法采用了高维凸几何的简单思想。新定理保证了这种超图中独立集的容器的较小族的存在，这使我们能够改进极值图论、离散几何和拉姆齐理论中几个问题的目前已知的最佳边界。

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An efficient container lemma

We prove a new, efficient version of the hypergraph container theorems that is suited for hypergraphs with large uniformities. The main novelty is a refined approach to constructing containers that employs simple ideas from high-dimensional convex geometry. The existence of smaller families of containers for independent sets in such hypergraphs, which is guaranteed by the new theorem, allows us to improve upon the best currently known bounds for several problems in extremal graph theory, discrete geometry, and Ramsey theory.

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来源期刊

Discrete Analysis Mathematics-Algebra and Number Theory

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

17 weeks

期刊介绍： Discrete Analysis is a mathematical journal that aims to publish articles that are analytical in flavour but that also have an impact on the study of discrete structures. The areas covered include (all or parts of) harmonic analysis, ergodic theory, topological dynamics, growth in groups, analytic number theory, additive combinatorics, combinatorial number theory, extremal and probabilistic combinatorics, combinatorial geometry, convexity, metric geometry, and theoretical computer science. As a rough guideline, we are looking for papers that are likely to be of genuine interest to the editors of the journal.