In this paper, we find explicit formulas or generating functions for the cardinalities of the sets Sn(T, τ ) of all permutations in Sn that avoid a pattern τ ∈ Sk and a set T , |T | ≥ 2, of patterns from S3. The main body of the paper is divided into three sections corresponding to the cases |T | = 2, 3 and |T | ≥ 4. As an example, in the fifth section, we obtain the complete classification of ...
