A generalization of Frieman's 3k-3 theorem

TL;DR

This paper extends Frieman's 3k-3 theorem to a broader class of sumsets, providing a more general understanding of their structure and properties in additive combinatorics.

Contribution

The paper introduces a generalized version of Frieman's 3k-3 theorem applicable to complex sumsets involving multiple sets and sum operations.

Findings

Proves a new bound for sumsets involving multiple sets.

Extends classical results to more general sumset configurations.

Provides insights into the structure of sumsets in additive number theory.

Abstract

We prove a generalization of Frieman's $3k-3$ theorem for the sumset $$ \Sigma^{l}(A_1,\ldots,A_k)=\{a_{j_{1}}+\cdots+a_{j_{l}}:\,1\leq j_{1}<\cdots<j_{l}\leq k,\ a_{j_{s}}\in A_{j_{s}}\text{ for all }s\}. $$