nelson-hadwiger problem

Fourier analysis, linear programming, and densities of distance avoiding sets in R^n

  • Fernando Mário de Oliveira Filho
  • Frank Vallentin
    • Categories Linear, Cone and Semidefinite Programming Tags , , ,

    In this paper we derive new upper bounds for the densities of measurable sets in R^n which avoid a finite set of prescribed distances. The new bounds come from the solution of a linear programming problem. We apply this method to obtain new upper bounds for measurable sets which avoid the unit distance in dimensions … Read more

    Lower Bounds for Measurable Chromatic Numbers

  • Christine Bachoc
  • Fernando Mário de Oliveira Filho
  • Frank Vallentin
  • Gabriele Nebe
    • Categories Semi-definite Programming Tags , , , ,

    The Lov\’asz theta function provides a lower bound for the chromatic number of finite graphs based on the solution of a semidefinite program. In this paper we generalize it so that it gives a lower bound for the measurable chromatic number of distance graphs on compact metric spaces. In particular we consider distance graphs on … Read more