Enumeration of monochromatic three term arithmetic progressions in\n two-colorings of cyclic groups

2014/08/05 by Erik Sjöland, Sjöland, Erik
Computer Science · Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1408.1058

openalex publication_date 2014/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

One of the toughest problems in Ramsey theory is to determine the existence\nof monochromatic arithmetic progressions in groups whose elements have been\ncolored. We study the harder problem to not only determine the existence of\nmonochromatic arithmetic progressions, but to also count them. We reformulate\nthe enumeration in real algebraic geometry and then use state of the art\ncomputational methods in semidefinite programming and representation theory to\nderive sharp, or an explicit constant from sharp, lower bounds for the cyclic\ngroup of any order.\n

Citations

• Symmetry groups, semidefinite programs, and sums of squares

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