Octabasic Laguerre polynomials and permutation statistics

R. Simion, D. Stanton

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)297-329
Number of pages33
JournalJournal of Computational and Applied Mathematics
Volume68
Issue number1-2
DOIs
StatePublished - Apr 22 1996

Bibliographical note

Funding Information:
* Corresponding author. E-mail: simion@gwuvm.gwu.edu. 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.

Funding Information:
1 This author was partially supported by the Mittag-Leffier Institute and by NSF grants DMS90-01195 and DMS94-00510.

Keywords

  • Combinatorial statistics
  • Laguerre polynomials
  • Orthogonal polynomials
  • Partitions
  • Permutations
  • q-analog

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