Generalized Narayana Polynomials, Riordan Arrays and Lattice Paths

Barry, Paul and Hennessy, Aoife (2012) Generalized Narayana Polynomials, Riordan Arrays and Lattice Paths. Journal of Integer Sequences, 15. 12.4.8. ISSN 1530-7638

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Official URL: https://cs.uwaterloo.ca/journals/JIS/

Abstract

We study a family of polynomials in two variables, identifying them as the moments of a two-parameter family of orthogonal polynomials. The coefficient array of these orthogonal polynomials is shown to be an ordinary Riordan array. We express the generating function of the sequence of polynomials under study as a continued fraction, and determine the corresponding Hankel transform. An alternative characterization of the polynomials in terms of a related Riordan array is also given. This Riordan array is associated with Lukasiewicz paths. The special form of the production matrices is exhibited in both cases. This allows us to produce a bijection from a set of coloured Lukasiewicz paths to a set of coloured Motzkin paths. The polynomials studied generalize the notion of Narayana polynomial.

Item Type: Article
Departments or Groups: *NONE OF THESE*
Divisions: School of Science
Depositing User: Paul Barry
Date Deposited: 19 Nov 2012 15:46
Last Modified: 22 Aug 2016 10:26
URI: http://repository.wit.ie/id/eprint/2109

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