A combinatorial interpretation of the connection constants for persistent sequences of polynomials

Authors:
Ottavio M. D'Antona;Emanuele Munarini
Affiliations:
Dipartimento di Informatica e Comunicazione, Università degli Studi di Milano, Milano, Italy;Dipartimento di Matematica, Politecnico di Milano, Milano, Italy
Venue:
European Journal of Combinatorics
Year:
2005

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Abstract

We give a combinatorial interpretation of the connection constants for persistent sequences of polynomials in terms of weighted binary paths. In this way we give bijective proofs for many formulas which generalize several classical identities and recurrences, such as the upper index sum, the Lagrange and the Vandermonde sum and Euler's theorem on the coefficients of Gaussian coefficients.