Identities involving Narayana polynomials and Catalan numbers

Toufik Mansour; Yidong Sun

doi:10.1016/j.disc.2008.12.006

Identities involving Narayana polynomials and Catalan numbers

Toufik Mansour, Yidong Sun

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We first establish the result that the Narayana polynomials can be represented as the integrals of the Legendre polynomials. Then we represent the Catalan numbers in terms of the Narayana polynomials by three different identities. We give three different proofs for these identities, namely, two algebraic proofs and one combinatorial proof. Some applications are also given which lead to many known and new identities. Crown

Original language	English
Pages (from-to)	4079-4088
Number of pages	10
Journal	Discrete Mathematics
Volume	309
Issue number	12
DOIs	https://doi.org/10.1016/j.disc.2008.12.006
State	Published - 28 Jun 2009

Bibliographical note

Funding Information:
The authors are grateful to the anonymous referees for the helpful suggestions and comments. The second author was supported by The National Science Foundation of China (10801020).

Keywords

Catalan numbers
Inverse relations
Legendre polynomials
Narayana polynomials

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2008.12.006

Cite this

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title = "Identities involving Narayana polynomials and Catalan numbers",

abstract = "We first establish the result that the Narayana polynomials can be represented as the integrals of the Legendre polynomials. Then we represent the Catalan numbers in terms of the Narayana polynomials by three different identities. We give three different proofs for these identities, namely, two algebraic proofs and one combinatorial proof. Some applications are also given which lead to many known and new identities. Crown",

keywords = "Catalan numbers, Inverse relations, Legendre polynomials, Narayana polynomials",

author = "Toufik Mansour and Yidong Sun",

note = "Funding Information: The authors are grateful to the anonymous referees for the helpful suggestions and comments. The second author was supported by The National Science Foundation of China (10801020).",

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AU - Sun, Yidong

N1 - Funding Information: The authors are grateful to the anonymous referees for the helpful suggestions and comments. The second author was supported by The National Science Foundation of China (10801020).

PY - 2009/6/28

Y1 - 2009/6/28

N2 - We first establish the result that the Narayana polynomials can be represented as the integrals of the Legendre polynomials. Then we represent the Catalan numbers in terms of the Narayana polynomials by three different identities. We give three different proofs for these identities, namely, two algebraic proofs and one combinatorial proof. Some applications are also given which lead to many known and new identities. Crown

AB - We first establish the result that the Narayana polynomials can be represented as the integrals of the Legendre polynomials. Then we represent the Catalan numbers in terms of the Narayana polynomials by three different identities. We give three different proofs for these identities, namely, two algebraic proofs and one combinatorial proof. Some applications are also given which lead to many known and new identities. Crown

KW - Catalan numbers

KW - Inverse relations

KW - Legendre polynomials

KW - Narayana polynomials

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DO - 10.1016/j.disc.2008.12.006

M3 - Article

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JO - Discrete Mathematics

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ER -

Identities involving Narayana polynomials and Catalan numbers

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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