Urn sampling and a majorization inequality

[摘要] 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 X-n = ((A-n)(a)) and Y-n = ((B-n)(b)) form such a pair for any nonnegative integers A greater than or equal to a, B greater than or equal to b, and proved this result in the cases min{A, B} greater than or equal to a + b and -b less than or equal to A - B less than or equal to a. We complete the proof of the conjecture by proving the result under the assumption max{A, B} greater than or equal to a + b. (C) 1997 Academic Press.

[发布日期] 1997-07-01