Identities in combinatorics, I

on sorting two ordered sets

Research output: Contribution to journalArticle

15 Citations (Scopus)

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) 97-106 10 Discrete Mathematics 11 2 https://doi.org/10.1016/0012-365X(75)90001-1 Published - Jan 1 1975

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Binomial coefficient identities
Hypergeometric Series
Ordered pair
Ordered Set
Combinatorics
Sorting
Summation
Enumeration
Subset

All Science Journal Classification (ASJC) codes

• Theoretical Computer Science
• Discrete Mathematics and Combinatorics

Cite this

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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.",
author = "Andrews, {George E.}",
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doi = "10.1016/0012-365X(75)90001-1",
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journal = "Discrete Mathematics",
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publisher = "Elsevier",
number = "2",

}

In: Discrete Mathematics, Vol. 11, No. 2, 01.01.1975, p. 97-106.

Research output: Contribution to journalArticle

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