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Volume 22, No 2, 2015, P. 73-85

UDC 519.1
V. G. Sargsyan
Counting sumsets and differences in Abelian groups

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.

DOI: 10.17377/daio.2015.22.449

Vahe G. Sargsyan 1
1. Lomonosov Moscow State University,
1 Leninskie gory, 119991 Moscow, Russia
e-mail: vahe_sargsyan@ymail.com