On comparison of Aunu permutation pattern and generalized permutation patterns using Wilf-equivalence

Abstract

A large number of articles have been published in the last decade studying pattern avoidance on permutations. From the point of view of enumeration, one tries to examine permutations avoiding certain patterns according to their lengths. We tackle the problem of refining this enumeration by considering the statistics “first/last entry” in the case of generalized patterns as well as “first entry unity” in the case of Aunu patterns. We give results for classical patterns of type  (Aunu patterns) as well as for at least one of the mentioned statistics for every generalized pattern of type .