A Further Note on Runs in Independent Sequences
Robert T. Smythe · 2005
Abstract. 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 conjec-ture of a previous paper (Smythe, 2003) concerning the expectation of this length is verified. 1