Geodesic
On partition polynomials
Diskretnaya Matematika, Tome 13 (2001) no. 2, pp. 144-158.

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

We consider some partition polynomials such that partial Bell and Platonov polynomials, generalised $A$- and $B$-polynomials, Touchard $T$- and $C$-polynomials, and $P$-polynomials which compose a quasi-orthogonal system with $T$-polynomials. We investigate the properties of the coefficients of these polynomials, present recurrence relations and combinatorial interpretations. For $C$-polynomials, we give recurrence relations, generating functions, and explicit expressions. 
@article{DM_2001_13_2_a7,
     author = {O. V. Kuz'min and O. V. Leonova},
     title = {On partition polynomials},
     journal = {Diskretnaya Matematika},
     pages = {144--158},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2001_13_2_a7/}
}
TY  - JOUR
AU  - O. V. Kuz'min
AU  - O. V. Leonova
TI  - On partition polynomials
JO  - Diskretnaya Matematika
PY  - 2001
SP  - 144
EP  - 158
VL  - 13
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2001_13_2_a7/
LA  - ru
ID  - DM_2001_13_2_a7
ER  - 
%0 Journal Article
%A O. V. Kuz'min
%A O. V. Leonova
%T On partition polynomials
%J Diskretnaya Matematika
%D 2001
%P 144-158
%V 13
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2001_13_2_a7/
%G ru
%F DM_2001_13_2_a7
O. V. Kuz'min; O. V. Leonova. On partition polynomials. Diskretnaya Matematika, Tome 13 (2001) no. 2, pp. 144-158. http://geodesic.mathdoc.fr/item/DM_2001_13_2_a7/

[1] Bell E. F., “Exponential polynomials”, Ann. Math., 35 (1934), 258–277 | DOI | MR | Zbl

[2] Riordan Dzh., Vvedenie v kombinatornyi analiz, IL, Moskva, 1963

[3] Kuzmin O. V., “Rekurrentnye sootnosheniya i perechislitelnye interpretatsii nekotorykh kombinatornykh chisel i polinomov”, Diskretnaya matematika, 6:3 (1994), 39–49 | MR | Zbl

[4] Zhukov V. D., “Rekurrentnye formuly dlya obobschennykh $A$- i $B$-polinomov”, Issledovaniya po geomagnetizmu, aeronomii i fizike Solntsa, Nauka, Moskva, 1983, 192–197

[5] Comtet L., Advanced Combinatorics, Reidel, Dordrecht, 1974 | MR | Zbl

[6] Howard F. T., “Bell polynomials and degenerate Stirling numbers”, Rend. Sem. Math. Univ. Padova., 61 (1980), 203–219 | MR

[7] Selivanov B. I., “Kombinatornyi podkhod k formule obrascheniya Byurmana–Lagranzha”, Kombinatornyi i asimptoticheskii analiz, 1977, 153–169, Izd-vo Krasnoyarskogo univ., Krasnoyarsk | MR

[8] Kuzmin O. V., “Postroenie obobschennykh $A$- i $B$-polinomov v prostranstve otobrazhenii”, Metody diskretnogo analiza v teorii grafov i slozhnosti, 52 (1992), 66–76, Institut Matem. SO RAN, Novosibirsk | MR

[9] Touchrd J., “Sur les cycles des substitutious”, Acta Math., 70 (1939), 243–279 | DOI | MR

[10] Chrysaphinou O., On Touchard polynomials, Discrete Math., 54, 1985 | DOI | MR | Zbl

[11] Charalambides Ch. A., Chrysaphinou O., “Partition polynomials in fluctuation theory”, Math. Nachr., 106 (1982), 89–100 | DOI | MR | Zbl

[12] Kuzmin O. V., Leonova O. V., “O polinomakh Tushara”, Asimptoticheskie i perechislitelnye zadachi kombinatornogo analiza, Izd-vo Irkutskogo univ., Irkutsk, 1997, 101–109

[13] Kuzmin O. V., Leonova O. V., “Polinomy Tushara i ikh prilozheniya”, Diskretnaya matematika, 12:3 (2000), 60–71 | Zbl

[14] Kuzmin O. V., Leonova O. V., “Polinomy Tushara i im kvaziortogonalnye”, Optimizatsiya, upravlenie, intellekt, 3 (1999), 218–227, IDSTU SO RAN, Irkutsk

[15] Dokin V. N., Zhukov V. D., Kolokolnikova N. A., Kuzmin O. V., Platonov M. L., Kombinatornye chisla i polinomy v modelyakh diskretnykh raspredelenii, Izd-vo Irkutskogo univ., Irkutsk, 1990 | MR | Zbl

[16] Platonov M. L., “Kombinatornye chisla klassa otobrazhenii”, Kombinatornyi i asimptoticheskii analiz, 1975, 81–85, Izd-vo Krasnoyarskogo univ., Krasnoyarsk | MR

[17] Platonov M. L., Kombinatornye chisla klassa otobrazhenii i ikh prilozheniya, Nauka, Moskva, 1979 | MR

[18] Kuzmin O. V., Obobschennye piramidy Paskalya i ikh prilozheniya, Nauka, Novosibirsk, 2000 | MR