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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Published in:	Electronic notes in discrete mathematics Vol. 54; pp. 313 - 318
Main Authors:	Jiménez, M. José, Encinas, Andrés M.
Format:	Journal Article Publication
Language:	English
Published:	Elsevier B.V 01.10.2016
Subjects:	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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Abstract	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.
AbstractList	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. 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 with the solution of linear three–terms recurrences. We show through some simple examples how this triangular arrays appear as essential components in the expression of some classical orthogonal polynomials and combinatorial numbers Peer Reviewed
Author	Encinas, Andrés M. Jiménez, M. José
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References	Spivey (br0080) 2011; 14 Graham, Knuth, Patashnik (br0030) 1994 Rainville (br0070) 1960 Došlić (br0020) 2005; 4 Mason, Handscomb (br0050) 2003 Neuwirth (br0060) 2001; 239 Liu, Wang (br0040) 2007; 39 Barbero, Salas, Villaseñor (br0010) 2014; 125 Liu (10.1016/j.endm.2016.09.054_br0040) 2007; 39 Barbero (10.1016/j.endm.2016.09.054_br0010) 2014; 125 Mason (10.1016/j.endm.2016.09.054_br0050) 2003 Došlić (10.1016/j.endm.2016.09.054_br0020) 2005; 4 Neuwirth (10.1016/j.endm.2016.09.054_br0060) 2001; 239 Spivey (10.1016/j.endm.2016.09.054_br0080) 2011; 14 Graham (10.1016/j.endm.2016.09.054_br0030) 1994 Rainville (10.1016/j.endm.2016.09.054_br0070) 1960
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Snippet	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... 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...
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SubjectTerms	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
Title	Combinatorial Recurrences and Linear Difference Equations
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