### Abstract

A binomial coefficient identity equivalent to Saalschutz's summation of a _{3}F_{2} 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) |
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Pages (from-to) | 97-106 |

Number of pages | 10 |

Journal | Discrete Mathematics |

Volume | 11 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1975 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

### Cite this

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*Discrete Mathematics*, vol. 11, no. 2, pp. 97-106. https://doi.org/10.1016/0012-365X(75)90001-1

**Identities in combinatorics, I : on sorting two ordered sets.** / Andrews, George E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Identities in combinatorics, I

T2 - on sorting two ordered sets

AU - Andrews, George E.

PY - 1975/1/1

Y1 - 1975/1/1

N2 - 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.

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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UR - http://www.scopus.com/inward/citedby.url?scp=0242704798&partnerID=8YFLogxK

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

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

M3 - Article

VL - 11

SP - 97

EP - 106

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 2

ER -