Permutations restricted by patterns of type (2, 1)

Recently, Babson and Steingrímsson (see [BS]) introduced generalized permutations patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. In this paper we study the generating functions for the number of permutations on n letters avoiding a generalized pattern ab-c where (a, b, c) ∈ S₃, and containing a prescribed number of occurrences of a generalized pattern cd-e where (c, d, e) ∈ S₃. As a consequence, we derive all the previously known results for this kind of problem, as well as many new results.