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arXiv · 2509.17013

On the partition regularity of arithmetic progressions and linear equations in k-IP-sets

Raphaël Giordano
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Abstract

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.

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Raphaël Giordano. 2025-09-21. On the partition regularity of arithmetic progressions and linear equations in k-IP-sets. https://arxiv.org/abs/2509.17013

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