A Direct Combinatorial Proof of a Positivity Result

J. Gillis; D. Zeilberger

doi:10.1016/S0195-6698(83)80015-8

A Direct Combinatorial Proof of a Positivity Result

J. Gillis, D. Zeilberger

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

5 Scopus citations

Abstract

Objects lying in four different boxes are rearranged in such a way that the number of objects in each box stays the same. Askey, Ismail, and Koornwinder proved that the cardinality of the set of rearrangements for which the number of objects changing boxes is even exceeds the cardinality of the set of rearrangements for which that number is odd. We give a simple counting proof of this fact.

Original language	English (US)
Pages (from-to)	221-223
Number of pages	3
Journal	European Journal of Combinatorics
Volume	4
Issue number	3
DOIs	https://doi.org/10.1016/S0195-6698(83)80015-8
State	Published - 1983
Externally published	Yes

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1016/S0195-6698(83)80015-8

Cite this

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abstract = "Objects lying in four different boxes are rearranged in such a way that the number of objects in each box stays the same. Askey, Ismail, and Koornwinder proved that the cardinality of the set of rearrangements for which the number of objects changing boxes is even exceeds the cardinality of the set of rearrangements for which that number is odd. We give a simple counting proof of this fact.",

author = "J. Gillis and D. Zeilberger",

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AB - Objects lying in four different boxes are rearranged in such a way that the number of objects in each box stays the same. Askey, Ismail, and Koornwinder proved that the cardinality of the set of rearrangements for which the number of objects changing boxes is even exceeds the cardinality of the set of rearrangements for which that number is odd. We give a simple counting proof of this fact.

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A Direct Combinatorial Proof of a Positivity Result

Abstract

All Science Journal Classification (ASJC) codes

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