How homogeneous can the last appearing pattern be?

Given a sequence of indepent, uniformly distributed random letters coming from a finite alphabet, we are interested in the word (pattern) which is the last to be observed for the first time among all words of length n. We derive anas. result on the homogeneity of this last appearing pattern as a corollary of a more general theorem. © 1993 John Wiley & Sons, Inc.