Geodesic
A formula for the number of combinations with constrained repetitions and its application
Prikladnaâ diskretnaâ matematika, no. 2 (2013), pp. 71-77.

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Various generalizations of the concept of combination with repetitions are obtained. Formulas for the calculation of the considered combinatorial numbers are found, and various problems that are solved with their application are considered.
Keywords: combinations with constrained repetitions, generating functions, multisets.
Mots-clés : Diophantine equations, formal polynomial 
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V. V. Gotsulenko. A formula for the number of combinations with constrained repetitions and its application. Prikladnaâ diskretnaâ matematika, no. 2 (2013), pp. 71-77. http://geodesic.mathdoc.fr/item/PDM_2013_2_a7/

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

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

[3] Petrovskii A. B., Prostranstva mnozhestv i multimnozhestv, URSS, M., 2003, 248 pp.

[4] MacMahon P. A., Combinatory analysis, The University Press, Cambridge, 1915, 296 pp.

[5] Juric Z., Siljak H., “A new formula for the number of combinations and permutations of multisets”, Appl. Math. Sci., 5:18 (2011), 875–881 | MR | Zbl

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

[7] Polia G., Sege G., Zadachi i teoremy iz analiza, Nauka, M., 1978, 391 pp.