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On Some Alternative Characterizations of Riordan Arrays

Published online by Cambridge University Press:  20 November 2018

Donatella Merlini ,
Douglas G. Rogers ,
Renzo Sprugnoli  and
M. Cecilia Verri
Donatella Merlini
Affiliation:
Dipartimento di Sistemi e Informatica, via Lombroso 6/17, 50134 Firenze, Italy e-mail: dada@dsi2.ing.unifi.it
Douglas G. Rogers
Affiliation:
Fernley House, The Green Croxley Green United Kingdom WD3 3HT e-mail: drogers@cs.bgsu.edu
Renzo Sprugnoli
Affiliation:
Dipartimento di Sistemi e Informatica via Lombroso 6/17 50134 Firenze, Italy e-mail: resp@ingfi1.ing.unifi.it
M. Cecilia Verri
Affiliation:
Dipartimento di Sistemi e Informatica via Lombroso 6/17 50134 Firenze, Italy e-mail: verri@ingfi1.ing.unifi.it
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Abstract

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We give several new characterizations of Riordan Arrays, the most important of which is: if {dn,k}n,k∈N is a lower triangular arraywhose generic element dn,k linearly depends on the elements in a well-defined though large area of the array, then {dn,k}n,k∈N is Riordan. We also provide some applications of these characterizations to the lattice path theory.

Keywords

05A1505C38
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 2 , 01 April 1997 , pp. 301 - 320
Copyright
Copyright © Canadian Mathematical Society 1997

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