向量空间和其他阿贝尔群中的完全3项等差数列自由小集

IF 0.9 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A Pub Date : 2025-04-30 DOI:10.1016/j.jcta.2025.106061

Bence Csajbók , Zoltán Lóránt Nagy

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引用次数: 0

摘要

如果阿贝尔群G的子集S不包含三个等差数列，则称为3-AP自由子集S。另外，如果S是最大的w.r.t.集合包含，则称为完全3-AP自由。加性组合学中最核心的问题之一是确定一个3-AP自由集合的最大大小，该集合必须是完全的。本文主要研究3-AP完全自由集的最小尺寸问题。我们定义并研究了3-AP的饱和，给出了若干向量空间族和循环群的小完全3-AP自由集和3-AP饱和集的构造。

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Complete 3-term arithmetic progression free sets of small size in vector spaces and other abelian groups

A subset S of an abelian group G is called 3-AP free if it does not contain a three term arithmetic progression. Moreover, S is called complete 3-AP free, if it is maximal w.r.t. set inclusion. One of the most central problems in additive combinatorics is to determine the maximal size of a 3-AP free set, which is necessarily complete. In this paper we are interested in the minimum size of complete 3-AP free sets. We define and study saturation w.r.t. 3-APs and present constructions of small complete 3-AP free sets and 3-AP saturating sets for several families of vector spaces and cyclic groups.

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来源期刊

Journal of Combinatorial Theory Series A 数学-数学

CiteScore

2.90

自引率

9.10%

发文量

审稿时长

12 months

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.