The box parameter for words and permutations

Abstract

The box parameter for words counts how often two letters and define a "box" such that all the letters +1 −1 fall into that box. It is related to the visibility parameter and other parameters on words. Three models are considered: Words over a finite alphabet, permutations, and words with letters following a geometric distribution. A typical result is: The average box parameter for words over an M letter alphabet is asymptotically given by 2 − 2 H M /M, for fixed M and → ∞. MSC:05A05, 05A30