Infinite Sum-Product Configurations in Parallel
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866916042377265152 |
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| author | Griffin, Conner |
| author_facet | Griffin, Conner |
| contents | We show that for any finite partition of $\mathbb{N}$ there is an infinite sequence whose finite sums are monochromatic and such that infinitely many of the products with a fixed number of factors are monochromatic -- though not necessarily belonging to the same color class as the finite sums. We are able to build these infinite configurations in parallel by refining arbitrary partitions of $\mathbb{N}$. We apply these techniques to prove that many complex infinite sum-product configurations are guaranteed to be monochromatic for arbitrary finite colorings of $\mathbb{N}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24751 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Infinite Sum-Product Configurations in Parallel Griffin, Conner Combinatorics We show that for any finite partition of $\mathbb{N}$ there is an infinite sequence whose finite sums are monochromatic and such that infinitely many of the products with a fixed number of factors are monochromatic -- though not necessarily belonging to the same color class as the finite sums. We are able to build these infinite configurations in parallel by refining arbitrary partitions of $\mathbb{N}$. We apply these techniques to prove that many complex infinite sum-product configurations are guaranteed to be monochromatic for arbitrary finite colorings of $\mathbb{N}$. |
| title | Infinite Sum-Product Configurations in Parallel |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.24751 |