Self-similarity in the combinatorial theory of orthogonal polynomials
type: Item
instance of: scholarly article
title: Self-similarity in the combinatorial theory of orthogonal polynomials
zbMATH Open document ID: 0804.05075
DOI: 10.1016/0304-3975(93)90310-P
author: Ivan Constantineau
published in: Theoretical Computer Science
publication date: 1993-12-15T00:00:00Z
review text: The author considers species of weighted combinatorial structures \(F\) associated to certain families of orthogonal polynomials (i.e. species \(F\) and the corresponding family have the same exponential generating function) and deals with the problem to determine the total weight \(\text{fix} (F[\beta])\) of all \(F\)-structures which are kept fixed by the action of a given permutation \(\beta\). The method used for this calculation is the so-called principle of autosimilarity which is demonstrated for some species associated to the Hermite and Laguerre polynomials, respectively. Furthermore, results relating to \(\text{fix} (F[\beta])\) are presented for species \(F\) associated to polynomials of Krawtchouk, Meixner, Meixner-Pollaczek and Jacobi. In these cases the weights correspond to orthogonal polynomials for suitable parameters.
Mathematics Subject Classification ID: 05E35
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 438328
zbMATH Keywords: species
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: weight
zbMATH Keywords: permutation
zbMATH Keywords: autosimilarity
reviewed by: Günter Schaar
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 438328