Combinatorial numbers of the finite multiset partitions
Prikladnaâ diskretnaâ matematika, no. 4 (2013), pp. 67-72.

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

The problem of determining the number of different partitions of any finite multiset is considered. The generating functions for these combinatorial numbers are found and some of its properties are stated.
Mots-clés : multiset partitions, Diophantine equations
Keywords: generating functions.
@article{PDM_2013_4_a6,
     author = {V. V. Gotsulenko},
     title = {Combinatorial numbers of the finite multiset partitions},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {67--72},
     publisher = {mathdoc},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2013_4_a6/}
}
TY  - JOUR
AU  - V. V. Gotsulenko
TI  - Combinatorial numbers of the finite multiset partitions
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2013
SP  - 67
EP  - 72
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2013_4_a6/
LA  - ru
ID  - PDM_2013_4_a6
ER  - 
%0 Journal Article
%A V. V. Gotsulenko
%T Combinatorial numbers of the finite multiset partitions
%J Prikladnaâ diskretnaâ matematika
%D 2013
%P 67-72
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2013_4_a6/
%G ru
%F PDM_2013_4_a6
V. V. Gotsulenko. Combinatorial numbers of the finite multiset partitions. Prikladnaâ diskretnaâ matematika, no. 4 (2013), pp. 67-72. http://geodesic.mathdoc.fr/item/PDM_2013_4_a6/

[1] Stenli R., Perechislitelnaya kombinatorika, Mir, M., 1990, 400 pp. | MR

[2] Novikov F. A., Diskretnaya matematika dlya programmistov, Piter, SPb., 2009, 384 pp.

[3] Vilenkin N. Ya., Kombinatorika, Nauka, M., 1969, 323 pp. | MR | Zbl

[4] Zatorskii R. A., “Podschet $m$-podmultimnozhestv cherez ikh vtorichnye spetsifikatsii”, Kombinatornyi analiz, 7, ed. K. A. Rybnikov, MGU, M., 1986, 136–145 | MR

[5] Gotsulenko V. V., “Formula dlya chisla sochetanii s povtoreniyami pri ogranicheniyakh i eë primenenie”, Prikladnaya diskretnaya matematika, 2013, no. 2(20), 71–77

[6] Yablonskii S. V., Vvedenie v diskretnuyu matematiku, Nauka, M., 1986, 384 pp. | MR