On a conjecture of Terry and Wolf
Combinatorics
2024-11-11 v1 Logic
Abstract
This paper shows that the -dimension of a subset of known as the 'quadratic Green-Sanders example' is at least 3 and at most 501. The upper bound confirms a conjecture of Terry and Wolf, who introduced this set in their recent work concerning strengthenings of the higher-order arithmetic regularity lemma under certain model-theoretic tameness assumptions. Additionally, the paper presents a simplified proof that the (linear) Green-Sanders example, which has its roots in Ramsey theory, has -dimension at most 3.
Cite
@article{arxiv.2411.05612,
title = {On a conjecture of Terry and Wolf},
author = {V. Gladkova},
journal= {arXiv preprint arXiv:2411.05612},
year = {2024}
}