A note on the Brown--Erdős--Sós conjecture in groups release_2qfonnctpbf3pcx4grizgw5n7m

by Jason Long

Released as a article .

2019  

Abstract

We show that a dense subset of a sufficiently large group multiplication table contains either a large part of the addition table of the integers modulo some k, or the entire multiplication table of a certain large abelian group, as a subgrid. As a consequence, we show that triples systems coming from a finite group contain configurations with t triples spanning O(√(t)) vertices, which is the best possible up to the implied constant. We confirm that for all t we can find a collection of t triples spanning at most t+3 vertices, resolving the Brown--Erdős--Sós conjecture in this context. The proof applies well-known arithmetic results including the multidimensional versions of Szemerédi's theorem and the density Hales--Jewett theorem.
In text/plain format

Archived Files and Locations

application/pdf  144.8 kB
file_pc5c7h6lqjf35mh2bzhhub2oyy
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2019-04-09
Version   v3
Language   en ?
arXiv  1902.07693v3
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 501a71de-33e0-4fae-b9a2-5ac200a43e83
API URL: JSON