Infinite linear patterns in sets of positive density
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911502416478208 |
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| author | Hernández, Felipe |
| author_facet | Hernández, Felipe |
| contents | In this article we describe all possible infinite linear configurations that can be found in a shift of any set of positive upper Banach density. This simultaneously generalizes Szemerédi's theorem on arithmetic progressions and the recent density finite sums theorem of Kra, Moreira, Richter, and Robertson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15458 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite linear patterns in sets of positive density Hernández, Felipe Dynamical Systems Combinatorics Number Theory 37A44 37B20 05D10 In this article we describe all possible infinite linear configurations that can be found in a shift of any set of positive upper Banach density. This simultaneously generalizes Szemerédi's theorem on arithmetic progressions and the recent density finite sums theorem of Kra, Moreira, Richter, and Robertson. |
| title | Infinite linear patterns in sets of positive density |
| topic | Dynamical Systems Combinatorics Number Theory 37A44 37B20 05D10 |
| url | https://arxiv.org/abs/2505.15458 |