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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.05612 |
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| _version_ | 1866917831621214208 |
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| author | Gladkova, V. |
| author_facet | Gladkova, V. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05612 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a conjecture of Terry and Wolf Gladkova, V. Combinatorics Logic 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. |
| title | On a conjecture of Terry and Wolf |
| topic | Combinatorics Logic |
| url | https://arxiv.org/abs/2411.05612 |