We study samples T = (T1.....Tn) of length n where the letters Fi are independently generated according to the geometric distribution F(Fj = i) = pqi-1, for 1≤ j ≤n, with p + q=1 and 0<p<1. An up-smooth sample F is a sample such that F i+1-Fi ≤1. We find generating functions for the probability that a sample of n geometric variables is up-smooth, with or without a specified first letter. We also extend the up-smooth results to words over an alphabet of k letters and to compositions of integers. In addition we study smooth samples F of geometric random variables, where the condition now is Fi+1F<i |≤ 1.
|Number of pages||13|
|Journal||Journal of Combinatorial Mathematics and Combinatorial Computing|
|State||Published - Nov 2012|
ASJC Scopus subject areas
- Mathematics (all)