On the Distribution of Monochromatic Complete Subgraphs and Arithmetic Progressions

On the Distribution of Monochromatic Complete Subgraphs and Arithmetic Progressions

We investigate the distributions of the number of: (1) monochromatic complete subgraphs over edgewise 2-colorings of complete graphs; and (2) monochromatic arithmetic progressions over 2-colorings of intervals, as statistical Ramsey theory questions. We present convincing evidence that both distribu...

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Veröffentlicht in:Experimental mathematics 2021-01, Vol.30 (1), p.135-145
Hauptverfasser: Robertson, Aaron, Cipolli, William, Dascălu, Maria
Format: Artikel
Sprache:eng
Schlagworte:
Delaporte distribution
monochromatic arithmetic progressions
monochromatic subgraphs
Ramsey's theorem
Van der Waerden's theorem
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Zusammenfassung:We investigate the distributions of the number of: (1) monochromatic complete subgraphs over edgewise 2-colorings of complete graphs; and (2) monochromatic arithmetic progressions over 2-colorings of intervals, as statistical Ramsey theory questions. We present convincing evidence that both distributions are very well-approximated by the Delaporte distribution.
ISSN:1058-6458
1944-950X
DOI:10.1080/10586458.2018.1507851