$B_h[g]$ modular sets from $B_h$ modular sets

Abstract

A set of positive integers $A$ is called a $B_h[g]$ set if there are at most $g$ different sums of $h$ elements from $A$ with the same result. This definition has a generalization to abelian groups and the main problem related to this kind of sets, is to find $B_h[g]$ maximal sets i.e. those with larger cardinality. We construct $B_h[g]$ modular sets from $B_h$ modular sets using homomorphisms and analyze the constructions of $B_h$ sets by Bose and Chowla, Ruzsa, and Gómez and Trujillo look at for the suitable homomorphism that allows us to preserve the cardinal of this types of sets.

References in corpus (1)

• Constructions of Generalized Sidon Sets