Identities in combinatorics, I: on sorting two ordered sets

George E. Andrews

doi:10.1016/0012-365X(75)90001-1

Identities in combinatorics, I: on sorting two ordered sets

George E. Andrews

Mathematics

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

19 Scopus citations

Abstract

A binomial coefficient identity equivalent to Saalschutz's summation of a ₃F₂ hypergeometric series is proved combinatorially. The proof depends on the enumeration of ordered pairs (A,B) of subsets of{1,2,3,...,ν} in which |A|=n, |B|=m, and B contains exactly r elements of the first n elements of A∪B.

Original language	English (US)
Pages (from-to)	97-106
Number of pages	10
Journal	Discrete Mathematics
Volume	11
Issue number	2
DOIs	https://doi.org/10.1016/0012-365X(75)90001-1
State	Published - 1975

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(75)90001-1

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title = "Identities in combinatorics, I: on sorting two ordered sets",

abstract = "A binomial coefficient identity equivalent to Saalschutz's summation of a 3F2 hypergeometric series is proved combinatorially. The proof depends on the enumeration of ordered pairs (A,B) of subsets of\{1,2,3,...,ν\} in which |A|=n, |B|=m, and B contains exactly r elements of the first n elements of A∪B.",

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AB - A binomial coefficient identity equivalent to Saalschutz's summation of a 3F2 hypergeometric series is proved combinatorially. The proof depends on the enumeration of ordered pairs (A,B) of subsets of{1,2,3,...,ν} in which |A|=n, |B|=m, and B contains exactly r elements of the first n elements of A∪B.

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U2 - 10.1016/0012-365X(75)90001-1

DO - 10.1016/0012-365X(75)90001-1

M3 - Article

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SP - 97

EP - 106

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 2

ER -

Identities in combinatorics, I: on sorting two ordered sets

Abstract

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