Geodesic
Counting sumsets and differences in abelian group
Diskretnyj analiz i issledovanie operacij, Tome 22 (2015) no. 2, pp. 73-85

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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, characteristic function, coset.
Mots-clés : group 
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     author = {V. G. Sargsyan},
     title = {Counting sumsets and differences in abelian group},
     journal = {Diskretnyj analiz i issledovanie operacij},
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     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2015_22_2_a5/}
}
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V. G. Sargsyan. Counting sumsets and differences in abelian group. Diskretnyj analiz i issledovanie operacij, Tome 22 (2015) no. 2, pp. 73-85. http://geodesic.mathdoc.fr/item/DA_2015_22_2_a5/