Refined Estimates Concerning Sumsets Contained in the Roots of Unity

Brandon Hanson; Giorgis Petridis

Refined Estimates Concerning Sumsets Contained in the Roots of Unity

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arxiv 1905.09134 v3 pith:BHWEWSEZ submitted 2019-05-22 math.NT math.CO

Refined Estimates Concerning Sumsets Contained in the Roots of Unity

Brandon Hanson , Giorgis Petridis This is my paper

classification math.NT math.CO

keywords additivecliqueco-sidoncomeconcerningcontaineddecompositionsestimates

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We prove that the clique number of the Paley graph is at most $\sqrt{p/2} + 1$, and that any supposed additive decompositions of the set of quadratic residues can only come from co-Sidon sets.

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Linear programming bounds for cliques in Paley graphs
math.CO 2019-07 unverdicted novelty 6.0

A linear programming bound obtained by restricting the Lovász theta number to local graphs of Paley graphs rivals the Hanson-Petridis closed-form bound and is conjectured to improve on it for infinitely many cases.