Estimates of the number of $(k,l)$-sumsets in the finite Abelian group

V. G. Sargsyan

Lomonosov Moscow State University

Abstract: The subset $A$ of the group $G$ is called $(k,l)$-sumset if there exists subset $B\subseteq G$ such that $A=kB-lB$, where $kB-lB=\{x_1 +\dots +x_k-x_{k+1}\dots - x_{k+l}\mid x_1,\dots, x_{k+l} \in B\}$. Upper and lower bounds of the number of $(k,l)$-sumsets in the Abelian group are obtained.

Keywords: arithmetic progression, group, characteristic function, coset.

UDC: 519.112.7

Received: 27.09.2015

DOI: 10.4213/dm1370

 English version: Discrete Mathematics and Applications, 2017, 27:4, 223–229

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