Year: 2024
Type: preprint
Abstract: This paper shows that the $\mathrm{VC}_2$-dimension of a subset of $\mathbb{F}_p^n$ 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 $\mathrm{VC}$-dimension at most 3.
Source: arXiv (Cornell University)
Author: Gladkova, V.
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404389897