Extremal Sidon sets are Fourier uniform, with applications to partition regularity

• Miquel Ortega ^[1] ; Sean Prendiville ^[2]
  1. [1] Universitat Politècnica de Catalunya

     Universitat Politècnica de Catalunya

     Barcelona, España

     
  2. [2] Lancaster University

     Lancaster University

     Lancaster, Reino Unido

     
• Localización: Discrete Mathematics Days 2022 / coord. por Luis Felipe Tabera Alonso, 2022, ISBN 978-84-19024-02-2, págs. 206-207
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Generalising results of Erd˝os-Freud and Lindstr¨om, we prove that the largest Sidonsubset of a bounded interval of integers is equidistributed in Bohr neighbourhoods. Weestablish this by showing that extremal Sidon sets are Fourier-pseudorandom, in that theyhave no large non-trivial Fourier coefficients. As a further application we deduce that, forany partition regular equation in five or more variables, every finite colouring of an extremalSidon set has a monochromatic solution.