Emeric Deutsch, Luca Ferrari, Simone Rinaldi
Published 2007-02-22Version 1
We translate the concept of succession rule and the ECO method into matrix notation, introducing the concept of a production matrix. This allows us to combine our method with other enumeration techniques using matrices, such as the method of Riordan matrices. Finally we treat the case of rational production matrices, i.e. those leading to rational generating functions.
Comments: accepted for publication on Annals of Combinatorics
Riordan arrays, the $A$-matrix, and Somos $4$ sequences
Catalan-like numbers and succession rules
Generalized Catalan recurrences, Riordan arrays, elliptic curves, and orthogonal polynomials
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