The conditional distribution of the longest run in a sample from a multiletter alphabet

Let be an ordered sequence of length of the members of a fixed set consisting of n i letters of type i,i - 1,...,k. The main result in this paper is a recursion based algorithm to compute the distribution function and/or p-values for the (conditional) distribution function of the longest run of any type in under the null hypothesis of random ordering in when n l ,..., n k are known. We demonstrate the utility of our algorithm using recur-sion and exact arithmetic in the software system Mathematica (Mathernatica is a registered trademark of Wolfram Research Incorporated).