English

On a conjecture of Terry and Wolf

Combinatorics 2024-11-11 v1 Logic

Abstract

This paper shows that the VC2\mathrm{VC}_2-dimension of a subset of Fpn\mathbb{F}_p^n 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 VC\mathrm{VC}-dimension at most 3.

Keywords

Cite

@article{arxiv.2411.05612,
  title  = {On a conjecture of Terry and Wolf},
  author = {V. Gladkova},
  journal= {arXiv preprint arXiv:2411.05612},
  year   = {2024}
}