Geodesic
Tilings of $p$-ary cyclic groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 562-565

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A tiling of a finite abelian group $G$ is a pair $(T , A)$ of subsets of $G$ such that every element $g \in G$ can be uniquely represented as $t+a$ with $t \in T$ , $a \in A$. In this paper we consider tilings of groups $\mathbb{Z}_{p^n}$ ($p$ is prime) and give a description of a recurrent scheme embracing all tilings of such groups. Furthermore we count their number.
Keywords: tiling, finite abelian group, factor group.
Mots-clés : set's kernel 
@article{SEMR_2013_10_a17,
     author = {D. K. Zhukov},
     title = {Tilings of $p$-ary cyclic groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {562--565},
     publisher = {mathdoc},
     volume = {10},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a17/}
}
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D. K. Zhukov. Tilings of $p$-ary cyclic groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 562-565. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a17/