• Riordan arrays associated with...

Result: Riordan arrays associated with Laurent series and generalized Sheffer-type groups

Title:
Riordan arrays associated with Laurent series and generalized Sheffer-type groups
Authors:
HE, Tian-Xiao
Source:
Linear algebra and its applications. 435(6):1241-1256
Publisher Information:
Amsterdam: Elsevier, 2011.
Publication Year:
2011
Physical Description:
print, 22 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Combinatoire, Combinatorics, Combinatoire algébrique, Algebraic combinatorics, Algèbre, Algebra, Algèbre linéaire et multilinéaire, matrices, Linear and multilinear algebra, matrix theory, Combinatoire énumérative, Enumerative combinatorics, Développement série, Series expansion, Desarrollo serie, Identité combinatoire, Combinatorial identity, Identidad combinatoria, Isomorphisme, Isomorphism, Isomorfismo, Nombre Stirling, Stirling number, Número Stirling, Polynôme Laurent, Laurent polynomial, Polinomio Laurent, Sous groupe, Subgroup, Subgrupo, Série entière, Power series, Serie potencias, Série exponentielle, 05A10, 05A15, 05A19, 05A30, Appell subgroup, Associated subgroup, Bell subgroup, Generalized Sheffer group, Generalized Stirling numbers, Hitting-time subgroup, Laurent series, Riordan arrays, Sheffer-type polynomial sequence
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics and Computer Science. Illinois Wesleyan University, Bloomington. IL 61702-2900, United States
ISSN:
0024-3795
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=24299043
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.24299043
Database:
PASCAL Archive

Further Information

A relationship between a pair of Laurent series and Riordan arrays is formulated. In addition, a type of generalized Sheffer groups is defined by using Riordan arrays with respect to power series with non-zero coefficients. The isomorphism between a generalized Sheffer group and the group of the Riordan arrays associated with Laurent series is established. Furthermore, Appell, associated, Bell, and hitting-time subgroups of the groups are defined and discussed. A relationship between the generalized Sheffer groups with respect to different type of power series is presented. The equivalence of the defined Riordan array pairs and generalized Stirling number pairs is given. A type of inverse relations of various series is constructed by using pairs of Riordan arrays. Finally, several applications involving various arrays, polynomial sequences, special formulas and identities are also presented as illustrative examples.