On the partition regularity of arithmetic progressions and linear equations in k-IP-sets
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914049711669248 |
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| author | Giordano, Raphaël |
| author_facet | Giordano, Raphaël |
| contents | In this paper, we provide versions of Van der Waerden's theorem and Rado's theorem for finite colorings of IP-sets and k-IP-sets. Here, by an IP-set we mean a set of integers that contains all finite sums of an infinite subset of N, and we define k-IP-sets similarly to IP-sets but allowing each summand to appear with multiplicity bounded by k - 1. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17013 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the partition regularity of arithmetic progressions and linear equations in k-IP-sets Giordano, Raphaël Combinatorics Number Theory In this paper, we provide versions of Van der Waerden's theorem and Rado's theorem for finite colorings of IP-sets and k-IP-sets. Here, by an IP-set we mean a set of integers that contains all finite sums of an infinite subset of N, and we define k-IP-sets similarly to IP-sets but allowing each summand to appear with multiplicity bounded by k - 1. |
| title | On the partition regularity of arithmetic progressions and linear equations in k-IP-sets |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2509.17013 |