Combinatorics of geometrically distributed random variables: Words and permutations avoiding two or three adjacent patterns

A word w = w(1)w(2)...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 single adjacent pattern was introduced. We investigate the probability that words and permutations of length n avoid two or three adjacent patterns.