Secretary Problem for Twins
by
Grzegorz Kubicki
University of Louisville, Louisville, KY 40292
Coauthors: Michal Morayne, Wroclaw University of Technology, Wroclaw, Poland

Consider a poset P consisting of two chains of the same length; the only uncomparable elements are elements from the same level, referred as twins. The elements of P are observed one-by-one in some random permutation. At any time we observe the partial order induced by the elements that came up to that moment. We want to choose the presently observed element maximizing the probability that this element is one of the two maximal twins. We find the optimal stopping time and establish the asymptotic behavior of the probability of success.

Date received: April 18, 2008