Monochromatic Sums and Products of Polynomials
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914925123731456 |
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| author | Alweiss, Ryan |
| author_facet | Alweiss, Ryan |
| contents | We show that the pattern $\{x,x+y,xy\}$ is partition regular over the space of formal integer polynomials of degree at least one with zero constant term, with primitive recursive bounds. This provides a new proof for the partition regularity of $\{x,x+y,xy\}$ over $\mathbb{N}$, which gives the first primitive recursive bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_00766 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Monochromatic Sums and Products of Polynomials Alweiss, Ryan Combinatorics Number Theory We show that the pattern $\{x,x+y,xy\}$ is partition regular over the space of formal integer polynomials of degree at least one with zero constant term, with primitive recursive bounds. This provides a new proof for the partition regularity of $\{x,x+y,xy\}$ over $\mathbb{N}$, which gives the first primitive recursive bound. |
| title | Monochromatic Sums and Products of Polynomials |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2211.00766 |