Geodesic
Estimates of the number of $(k,l)$-sumsets in the finite Abelian group
Diskretnaya Matematika, Tome 28 (2016) no. 2, pp. 71-80

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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. 
@article{DM_2016_28_2_a6,
     author = {V. G. Sargsyan},
     title = {Estimates of the number of $(k,l)$-sumsets in the finite {Abelian} group},
     journal = {Diskretnaya Matematika},
     pages = {71--80},
     publisher = {mathdoc},
     volume = {28},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2016_28_2_a6/}
}
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V. G. Sargsyan. Estimates of the number of $(k,l)$-sumsets in the finite Abelian group. Diskretnaya Matematika, Tome 28 (2016) no. 2, pp. 71-80. http://geodesic.mathdoc.fr/item/DM_2016_28_2_a6/