On the Inverse Erdos-Heilbronn Problem for Restricted Set Addition in Finite Groups

TL;DR

This paper surveys additive combinatorics results related to the Erdos-Heilbronn problem, introduces an open conjecture for nonabelian groups, and extends key theorems to composite and nonabelian group settings.

Contribution

It formulates a new open conjecture for the inverse Erdos-Heilbronn problem in nonabelian groups and generalizes existing theorems to broader group contexts.

Findings

Extended inverse Dias da Silva-Hamidoune theorem to Z/nZ with composite n

Generalized results to nonabelian groups

Formulated an open conjecture for inverse Erdos-Heilbronn problem in nonabelian groups

Abstract

We provide a survey of results concerning both the direct and inverse problems to the Cauchy-Davenport theorem and Erdos-Heilbronn problem in Additive Combinatorics. We formulate an open conjecture concerning the inverse Erdos-Heilbronn problem in nonabelian groups. We extend an inverse to the Dias da Silva-Hamidoune Theorem to Z/nZ where n is composite, and we generalize this result into nonabelian groups.