Enumerating Permutations Avoiding Three Babson-Steingrímsson Patterns

摘要

We settle some conjectures formulated by A. Claesson and T. Mansour concerning generalized pattern avoidance of permutations. In particular, we solve the problem of the enumeration of permutations avoiding three generalized patterns of type (1, 2) or (2, 1) by using ECO method and a graphical representation of permutations.