Extremal Sidon sets are Fourier uniform, with applications to partition regularity
Combinatorics
2021-10-27 v1 Number Theory
Abstract
Generalising results of Erd\H{o}s-Freud and Lindstr\"om, we prove that the largest Sidon subset of a bounded interval of integers is equidistributed in Bohr neighbourhoods. We establish this by showing that extremal Sidon sets are Fourier-pseudorandom, in that they have no large non-trivial Fourier coefficients. As a further application we deduce that, for any partition regular equation in five or more variables, every finite colouring of an extremal Sidon set has a monochromatic solution.
Keywords
Cite
@article{arxiv.2110.13447,
title = {Extremal Sidon sets are Fourier uniform, with applications to partition regularity},
author = {Miquel Ortega and Sean Prendiville},
journal= {arXiv preprint arXiv:2110.13447},
year = {2021}
}