Geodesic
Enumerating functions for nonnegative integer coordinates of $L$-dimensional vectors
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 1, pp. 147-155 
S. L. Chernyshev. Enumerating functions for nonnegative integer coordinates of $L$-dimensional vectors. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 1, pp. 147-155. http://geodesic.mathdoc.fr/item/FPM_2009_15_1_a10/
@article{FPM_2009_15_1_a10,
     author = {S. L. Chernyshev},
     title = {Enumerating functions for nonnegative integer coordinates of $L$-dimensional vectors},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {147--155},
     year = {2009},
     volume = {15},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2009_15_1_a10/}
}
TY  - JOUR
AU  - S. L. Chernyshev
TI  - Enumerating functions for nonnegative integer coordinates of $L$-dimensional vectors
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2009
SP  - 147
EP  - 155
VL  - 15
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/FPM_2009_15_1_a10/
LA  - ru
ID  - FPM_2009_15_1_a10
ER  - 
%0 Journal Article
%A S. L. Chernyshev
%T Enumerating functions for nonnegative integer coordinates of $L$-dimensional vectors
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2009
%P 147-155
%V 15
%N 1
%U http://geodesic.mathdoc.fr/item/FPM_2009_15_1_a10/
%G ru
%F FPM_2009_15_1_a10

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

The enumerating function $C^L(X_1,\dots,X_L)$, which bijectively maps tuples of length $L$ of nonnegative integers to nonnegative integers $Z=C^L(X_1,\dots,X_L)$, is represented as a sum of $L$ figurate numbers.

[1] Ershov Yu. L., Teoriya numeratsii, Nauka, M., 1977 | MR

[2] Ershov Yu. L., Goncharov S. S., Konstruktivnye modeli, Novosibirsk, 1999

[3] Yu. V. Prokhorov (red.), Matematicheskii entsiklopedicheskii slovar, Sovetskaya entsiklopediya, M., 1988 | MR | Zbl

[4] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, Nauka, M., 1982 | MR | Zbl

[5] Chernyshëv S. L., “Opisanie posledovatelnoi protsedury prinyatiya reshenii s pomoschyu kombinatornykh chisel”, Nadëzhnost i kachestvo, Trudy mezhdunarodnogo simpoziuma, ed. N. K. Yurkov, Izd-vo Penzenskogo gos. un.-ta, Penza, 2004

[6] Chernyshëv S. L., Chernyshëv L. S., “Kvantovyi analiz rezultatov izmerenii”, Izmeritelnaya tekhnika, 2006, no. 12, 3–8