Production Matrices and Riordan Arrays |
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| Authors: | Emeric Deutsch Luca Ferrari Simone Rinaldi |
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| Affiliation: | (1) Department of Mathematics, Polytechnic University, Six Metrotech Center, Brooklyn, New York, 11201, USA;(2) Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, Viale Morgagni 65, 50134 Firenze, Italy;(3) Dipartimento di Scienze Matematiche e Informatiche “Roberto Magari”, Università Degli Studi di Siena, Pian dei Mantellini, 44, 53100 Siena, Italy |
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| Abstract: | We translate the concept of succession rule and the ECO method into matrix notation, introducing the concept of 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. L. Ferrari and S. Rinaldi have been partially supported by MIUR project: Linguaggi formali e automi: metodi, modelli e applicazioni. |
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| Keywords: | ECO method production matrices Riordan arrays |
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