Probabilities for a Generalized Birthday Problem

Let 1's and M- 0's be randomly arranged in a row. Saperstein [11] defines the random variable k* m to be the maximum number of 1's within any m consecutive positions in the arrangement, and finds Pr (k* m < k) for k > . This article derives the distribution of k*m, for all for M/m = L, L an integer. Simplified forms are given for M/m = L, k > .