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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - D. K. Zhukov
TI  - Tilings of $p$-ary cyclic groups
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2013
SP  - 562
EP  - 565
VL  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2013_10_a17/
LA  - en
ID  - SEMR_2013_10_a17
ER  - 
%0 Journal Article
%A D. K. Zhukov
%T Tilings of $p$-ary cyclic groups
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2013
%P 562-565
%V 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2013_10_a17/
%G en
%F SEMR_2013_10_a17
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/

[1] G. Cohen, S. Litsyn, A. Vardy, G. Zemor, “Tilings of binary spaces”, SIAM J. Discrete Math., 9 (1996), 393–412 | DOI | MR | Zbl

[2] T. Etzion, A. Vardy, “On perfect codes and tilings: problems and solutions”, SIAM J. Discrete Math., 11 (1998), 205–223 | DOI | MR | Zbl

[3] M. Dinitz, “Full rank tilings of finite abelian groups”, SIAM J. Discrete Math., 20 (2006), 160–170 | DOI | MR | Zbl

[4] Sandor Szabo, Arthur D. Sands, Factoring groups into subsets, Taylor Francis Group, 2009 | MR

[5] Kenneth Ireland, Michael Rosen, A classical Introduction To Modern Number Theory, Springer-Verlag, New York, 1982 | MR