q-Analog of tableau containment

Abstract

We prove a q-analog of the following result due to McKay, Morse and Will: the probability that a random standard Young tableau of size n contains a fixed standard Young tableau of shape lambda proves k tends to f(lambda)/k! in the large n limit, where f(lambda) is the number of standard Young tableaux of shape A. We also consider the probability that a random pair (P, Q) of standard Young tableaux of the same shape contains a fixed pair (A, B) of standard Young tableaux. (C) 2010 Elsevier Inc. All rights reserved.