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

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.