R. T. Smythe ^{}

Given a sequence of letters generated independently from
a finite alphabet, we consider the case when more than one, but not
all, letters are generated with the highest probability. The length of
the longest run of any of these letters is shown to be one greater than
the length of the longest run in a particular state of an associated
Markov chain. Using results of Foulser and Karlin (1987), a conjecture
of a previous paper (Smythe, 2003) concerning the expectation
of this length is verified.

Received: 2011/10/22 | Accepted: 2015/09/12