Combinatorics of Geometrically Distributed Random Variables: Words and Permutations Avoiding Two or Three Adjacent Patterns

Abstract

A word \(w = w_1w_2\ldots w_n\) avoids an adjacent pattern \(\tau\) iff \(w\) has no subsequence of adjacent letters having all the same pairwise comparisons as \(\tau\). In [12] and [13] the concept of words and permutations avoiding a single adjacent pattern was introduced. We investigate the probability that words and permutations of length \(n\) avoid two or three adjacent patterns.