Restricted Product Sets under Unique Representability

TL;DR

This paper extends Kemperman--Scherk type results to restricted product sets in multiplicative groups of fields, utilizing polynomial methods to establish new bounds and properties.

Contribution

It introduces new Kemperman--Scherk type theorems for restricted product sets in multiplicative groups of fields using polynomial techniques.

Findings

Established bounds for restricted product sets in cyclic groups

Applied polynomial method to prove new combinatorial results

Extended classical results to broader algebraic structures

Abstract

We prove some results of Kemperman--Scherk type for restricted product sets in multiplicative groups of fields (in particular, for cyclic groups). The proofs use polynomial method.