Monochromatic sums and quotients in $\mathbb N$
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914504344862720 |
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| author | Di Nasso, Mauro Baglini, Lorenzo Luperi Mennuni, Rosario Ragosta, Mariaclara Vegnuti, Alessandro |
| author_facet | Di Nasso, Mauro Baglini, Lorenzo Luperi Mennuni, Rosario Ragosta, Mariaclara Vegnuti, Alessandro |
| contents | We prove partition regularity of the configuration $x,y,x+y,y/x$ in a strong infinitary form that extends Hindman's Theorem. We study the related issue of partition regularity of configurations involving products of a degree one polynomial in $x$ with one in $y$, reducing the general problem to a handful of special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03115 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monochromatic sums and quotients in $\mathbb N$ Di Nasso, Mauro Baglini, Lorenzo Luperi Mennuni, Rosario Ragosta, Mariaclara Vegnuti, Alessandro Logic Combinatorics Number Theory 05D10 (Primary) 26E35, 03H15, 11U10, 54D80 (Secondary) We prove partition regularity of the configuration $x,y,x+y,y/x$ in a strong infinitary form that extends Hindman's Theorem. We study the related issue of partition regularity of configurations involving products of a degree one polynomial in $x$ with one in $y$, reducing the general problem to a handful of special cases. |
| title | Monochromatic sums and quotients in $\mathbb N$ |
| topic | Logic Combinatorics Number Theory 05D10 (Primary) 26E35, 03H15, 11U10, 54D80 (Secondary) |
| url | https://arxiv.org/abs/2603.03115 |