Result: Hankel determinants of sums of consecutive weighted Schröder numbers
Title:
Hankel determinants of sums of consecutive weighted Schröder numbers
Authors:
Source:
Linear algebra and its applications. 437(9):2285-2299
Publisher Information:
Amsterdam: Elsevier, 2012.
Publication Year:
2012
Physical Description:
print, 24 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, Algèbre, Algebra, Algèbre linéaire et multilinéaire, matrices, Linear and multilinear algebra, matrix theory, Analyse régression, Regression analysis, Análisis regresión, Combinatoire énumérative, Enumerative combinatorics, Fonction génératrice, Generating function, Función generatriz, Fonction matricielle, Matrix function, Función matricial, Identité combinatoire, Combinatorial identity, Identidad combinatoria, Modélisation, Modeling, Modelización, Nombre réel, Real number, Número real, Treillis, Lattice, Enrejado, 05A19, 15A15, Hankel determinants, Lattice paths, Schroder numbers
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Tawain, Province of China
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Tawain, Province of China
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Tawain, Province of China
ISSN:
0024-3795
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
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.26255776
Database:
PASCAL Archive
Further Information
We consider weighted large and small Schröder paths with up steps (1, 1), down steps (1, ―1) assigned the weight of 1 and with level steps (2, 0) assigned the weight of t, where t is a real number. The weight of a path is the product of the weights of all its steps. Let r(t)ℓ and s(t)ℓ be the total weight of all weighted large and small Schröder paths from (0. 0) to (2ℓ, 0), respectively. For constants α, β, we derive the generating functions and the explicit formulae for the determinants of the Hankel matrices (ar(t)i+j―2 + βr(t)i+j―1)ni,j=1, (αr(t)i+j―1 + βr(t)i+j)ni,j=1, (αs(t)i+j―2 + βs(t)i+j―1)ni,j=1 and (αs(t)i+j―1 βs(t)i+j)ni,j=1 combinatorially via suitable lattice path models.