A set of orthogonal polynomials with eight independent "q's" is defined which generalizes the Laguerre polynomials. The moments of the measure for these polynomials are the generating functions for permutations according to eight different statistics. Specializing these statistics gives many other well-known sets of combinatorial objects and relevant statistics. The specializations are studied, with applications to classical orthogonal polynomials and equidistribution theorems for statistics.
Bibliographical noteFunding Information:
* Corresponding author. E-mail: firstname.lastname@example.org. This work was carried out in part during this author's visits at the Mittag-Lettler Institute and the University of Qu6bec at Montr6al, and with partial support through NSF grant DMS91-08749.
1 This author was partially supported by the Mittag-Leffier Institute and by NSF grants DMS90-01195 and DMS94-00510.
- Combinatorial statistics
- Laguerre polynomials
- Orthogonal polynomials