Infinite monochromatic patterns in the integers

2021/05/20 by Di Nasso, Mauro · 1 citation
#11B75 #Combinatorics (math.CO) #FOS: Mathematics #Primary 05D10 #Secondary 03E05

paper · doi:10.48550/arxiv.2105.09541

Abstract

We show the existence of several infinite monochromatic patterns in the integers obtained as values of suitable symmetric polynomials. The simplest example is the following. For every finite coloring of the natural numbers ℕ=C₁∪…∪ C_r, there exists an increasing sequence a<b></b>

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• Hypernatural numbers in arithmetic Ramsey theory

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