Combinatorial Bounds in Distal Structures
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866910017914929152 |
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| author | Anderson, Aaron |
| author_facet | Anderson, Aaron |
| contents | We provide polynomial upper bounds for the minimal sizes of distal cell decompositions in several kinds of distal structures, particularly weakly $o$-minimal and $P$-minimal structures. The bound in general weakly $o$-minimal structures generalizes the vertical cell decomposition for semialgebraic sets, and the bounds for vector spaces in both $o$-minimal and $p$-adic cases are tight. We apply these bounds to Zarankiewicz's problem and sum-product bounds in distal structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_07769 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Combinatorial Bounds in Distal Structures Anderson, Aaron Logic Combinatorics 03C45 (Primary), 03C64, 05C35 (Secondary) We provide polynomial upper bounds for the minimal sizes of distal cell decompositions in several kinds of distal structures, particularly weakly $o$-minimal and $P$-minimal structures. The bound in general weakly $o$-minimal structures generalizes the vertical cell decomposition for semialgebraic sets, and the bounds for vector spaces in both $o$-minimal and $p$-adic cases are tight. We apply these bounds to Zarankiewicz's problem and sum-product bounds in distal structures. |
| title | Combinatorial Bounds in Distal Structures |
| topic | Logic Combinatorics 03C45 (Primary), 03C64, 05C35 (Secondary) |
| url | https://arxiv.org/abs/2104.07769 |