Counting (k,l)-sumsets in groups of prime order

TL;DR

This paper investigates the number of specific sumsets, called (k,l)-sumsets, within groups of prime order, providing bounds that enhance understanding of their structure and quantity.

Contribution

It introduces bounds on the number of (k,l)-sumsets in prime order groups, advancing the combinatorial understanding of sumset structures.

Findings

Established upper bounds for (k,l)-sumsets

Established lower bounds for (k,l)-sumsets

Enhanced understanding of sumset enumeration in prime groups

Abstract

A subset $A$ of a group $G$ is called $(k, l)$-{\it sumset}, if $A= kB-lB$ for some $B\subseteq G$, where $kB-lB={x_1+...+x_k-x_{k+1}-...-x_{k+l} : x_1,..., x_{k+l}\in B}.$ Upper and lower bounds for the number $(k, l)$-sumsets in groups of prime order are provided.