A Direct Combinatorial Proof of a Positivity Result

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

European Journal of Combinatorics

Volume 4, Issue 3, September 1983, Pages 221-223

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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.

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^†: Current address: Department of Mathematical Science, Drexel University, Philadelphia, PA 19104, U.S.A.