Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4673255 | Indagationes Mathematicae | 2009 | 17 Pages |
Abstract
This paper is concerned with the sequence q(n) recursively defined as q(2) = ¼ and q(n)=n−1n(1−21/(1−n)+q(n−1)n/(n−1)),n=3,4..., where each q(n) represents certain winning probability in a secretary problem with horizon n. We show that this sequence is concave, as well as subadditive and supermultiplicative in a strong sense. We also present several sharp inequalities implying in particular that q(n) converges towards its limit at the rate n−1, as n→∞.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
José A. Adell, Horst Alzer,