Year: 2026
Type: preprint
Abstract: 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 $\mathbb{N}$.
Source: arXiv (Cornell University)
Author: Griffin, Conner
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162398501