Combinatorial Recurrences and Linear Difference Equations

In this work we introduce the triangular arrays of depth greater than 1 given by linear recurrences, that generalize some well-known recurrences that appear in enumerative combinatorics. In particular, we focussed on triangular arrays of depth 2, since they are closely related to the solution of lin...

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Vydané v:	Electronic notes in discrete mathematics Ročník 54; s. 313 - 318
Hlavní autori:	Jiménez, M. José, Encinas, Andrés M.
Médium:	Journal Article Publikácia
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 01.10.2016
Predmet:	11 Number theory 11C Polynomials and matrices 39 Difference and functional equations 39A Difference equations Classificació AMS Combinatorial identities Difference equations Equacions diferencials i integrals Equacions en diferències Finite difference equations Matemàtiques i estadística Matrices Matrius (Matemàtica) Orthogonal polynomials Polinomis ortogonals Triangular matrices Àrees temàtiques de la UPC Combinatorial identities triangular matrices finite difference equations orthogonal polynomials
ISSN:	1571-0653, 1571-0653
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Popis
Shrnutí:	In this work we introduce the triangular arrays of depth greater than 1 given by linear recurrences, that generalize some well-known recurrences that appear in enumerative combinatorics. In particular, we focussed on triangular arrays of depth 2, since they are closely related to the solution of linear three–term recurrences. We show through some simple examples how these triangular arrays appear as essential components in the expression of some classical orthogonal polynomials and combinatorial numbers.
ISSN:	1571-0653 1571-0653
DOI:	10.1016/j.endm.2016.09.054