Construction of Bh[g] sets in product of groups

TL;DR

This paper introduces three new methods for constructing Bh[g] sets within product groups, expanding the toolkit for combinatorial and additive number theory research.

Contribution

It provides novel constructions of Bh[g] sets specifically tailored for product groups, which was not previously explored.

Findings

Three new constructions of Bh[g] sets in product groups

Enhanced understanding of additive properties in group products

Potential applications in combinatorics and number theory

Abstract

A subset A of an abelian group G is a Bh[g] set on G if every element of G can be written at most g ways as sum of h elements in A. In this work we present three constructions of Bh[g] sets on product of groups.