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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

Brandon Hanson , Giorgis Petridis This is my paper · ORCID
classification math.NTmath.CO
keywords additivecliqueco-sidoncomeconcerningcontaineddecompositionsestimates
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abstract

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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  1. A note on pseudorandom Ramsey graphs

    math.CO 2019-09 conditional novelty 7.0 of 10

    For fixed s, optimal K_s-free pseudorandom graphs would imply r(s,t)=t^{s-1+o(1)}, and new constructions improve the cycle Ramsey lower bounds to r(C5,t) > t^{11/8} and r(C7,t) > t^{11/9}.

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