Arithmetic subtrees in large subsets of products of trees
Combinatorics
2021-11-03 v1 Dynamical Systems
Abstract
Furstenberg-Weiss have extended Szemer\'edi's theorem on arithmetic progressions to trees by showing that a large subset of the tree contains arbitrarily long arithmetic subtrees. We study higher dimensional versions that analogously extend the multidimensional Szemer\'edi theorem by demonstrating the existence of certain arithmetic structures in large subsets of a cartesian product of trees.
Keywords
Cite
@article{arxiv.2111.01452,
title = {Arithmetic subtrees in large subsets of products of trees},
author = {Kamil Bulinski and Alexander Fish},
journal= {arXiv preprint arXiv:2111.01452},
year = {2021}
}
Comments
16 pages, no figures