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
Received 20 March 2014
Revised 9 September 2014
References
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