This article is cited in 4 papers

Counting sumsets and differences in abelian group

V. G. Sargsyan

Lomonosov Moscow State University, 1 Leninskie gory, 119991 Moscow, Russia

Abstract: A subset $A$ of a group $G$ is called $(k,l)$-sumset, if $A=kB-lB$ for some $B\subseteq G$, 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 for the numbers of $(1,1)$-sumsets and $(2,0)$-sumsets in abelian groups are provided. Bibliogr. 4.

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

UDC: 519.1

Received: 20.03.2014
Revised: 09.09.2014

DOI: 10.17377/daio.2015.22.449

 English version: Journal of Applied and Industrial Mathematics, 2015, 9:2, 275–282

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