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

2025/09/21 by Giordano, Raphaël
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2509.17013

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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