Sums of triples in Abelian groups

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2023-04-18 DOI:10.1112/mtk.12200

Ido Feldman, Assaf Rinot

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引用次数: 0

Abstract

Motivated by a problem in additive Ramsey theory, we extend Todorčević's partitions of three-dimensional combinatorial cubes to handle additional three-dimensional objects. As a corollary, we get that if the continuum hypothesis fails, then for every Abelian group G of size ℵ₂, there exists a coloring $c : G \to Z$ such that for every uncountable $X \subseteq G$ and every integer k, there are three distinct elements $x, y, z$ of X such that $c (x + y + z) = k$ .

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阿贝尔群中三元组的和

受加性拉姆齐理论中的一个问题的启发，我们扩展了Todorčević的三维组合立方体划分，以处理额外的三维对象。作为推论，我们得到，如果连续体假设失败，那么对于每个大小为G的阿贝尔群ℵ2，存在一个着色c:G→Z$c:G\rightarrow\mathbb｛Z｝$使得对于每个不可数X⊆G$X\substeqG$和每个整数k，X有三个不同的元素X，y，Z$X，y和Z$使得c（X+y+Z）=k$c（X+p+Z）=k$。

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.