Geodesic
Touchard $C$-polynomials and polynomials quasi-orthogonal to them
Diskretnaya Matematika, Tome 17 (2005) no. 2, pp. 153-159.

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

We consider the Touchard $C$-polynomials closely related to the cycle indices of symmetric groups and introduce the so-called $M$-polynomials. We demonstrate that the $C$- and $M$-polynomials constitute a quasi-orthogonal system. For the partition polynomials under consideration, we give a series of recurrence relations. 
@article{DM_2005_17_2_a13,
     author = {O. V. Kuz'min and O. V. Leonova},
     title = {Touchard $C$-polynomials and polynomials quasi-orthogonal to them},
     journal = {Diskretnaya Matematika},
     pages = {153--159},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2005_17_2_a13/}
}
TY  - JOUR
AU  - O. V. Kuz'min
AU  - O. V. Leonova
TI  - Touchard $C$-polynomials and polynomials quasi-orthogonal to them
JO  - Diskretnaya Matematika
PY  - 2005
SP  - 153
EP  - 159
VL  - 17
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2005_17_2_a13/
LA  - ru
ID  - DM_2005_17_2_a13
ER  - 
%0 Journal Article
%A O. V. Kuz'min
%A O. V. Leonova
%T Touchard $C$-polynomials and polynomials quasi-orthogonal to them
%J Diskretnaya Matematika
%D 2005
%P 153-159
%V 17
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2005_17_2_a13/
%G ru
%F DM_2005_17_2_a13
O. V. Kuz'min; O. V. Leonova. Touchard $C$-polynomials and polynomials quasi-orthogonal to them. Diskretnaya Matematika, Tome 17 (2005) no. 2, pp. 153-159. http://geodesic.mathdoc.fr/item/DM_2005_17_2_a13/

[1] Bell E. T., “Partition polynomials”, Ann. Math., 29 (1927), 38–46 | DOI | MR | Zbl

[2] Touchard J., “Sur les cycles des substitutions”, Acta Math., 70 (1939), 243–279 | DOI | MR

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

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

[5] Kuzmin O. V., Leonova O. V., “O polinomakh razbienii”, Diskretnaya matematika, 13:2 (2001), 144–158 | MR | Zbl

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

[7] Zhukov V. D., “Proizvodyaschii opredelitel”, Asimptoticheskie i perechislitelnye zadachi kombinatornogo analiza, Krasnoyarskii un-t, Krasnoyarsk, 1976, 47–58 | MR

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

[9] Kuzmin O. V., Leonova O. V., “Ob asimptoticheskoi sopryazhennosti polinomov Tushara”, Diskretnaya matematika, 14:1 (2002), 151–157 | MR