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Urn Sampling and a Majorization Inequality

Authors
Journal
Journal of Combinatorial Theory Series A
0097-3165
Publisher
Elsevier
Publication Date
Volume
79
Issue
1
Identifiers
DOI: 10.1006/jcta.1997.2773

Abstract

Abstract In the context of a certain urn-sampling game, Bennett has studied pairs of sequences for which the products of successive finite differences of the sequences are majorized by the differences of the termwise product of the sequences. Bennett conjectured that the sequences {\bf x}_n={A-n \choose a} and {\bf y}_n={B-n \choose b} form such a pair for any nonnegative integers A⩾ a, B⩾ b, and proved this result in the cases min{ A, B}⩾ a+ band − b⩽ A− B⩽ a. We complete the proof of the conjecture by proving the result under the assumption max{ A, B}⩾ a+ b.

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