A New Class of Wilf-Equivalent Permutations

Abstract

For about 10 years, the classification up to Wilf equivalence of permutation patterns was thought completed up to length 6. In this paper, we establish a new class of Wilf-equivalent permutation patterns, namely, (i>n − 1, i>n − 2, i>n, τ) ∼ (i>n − 2, i>n, i>n − 1, τ) for any τ∈i>Sn−3. In particular, at level i>n e 6, this result includes the only missing equivalence (546213) ∼ (465213), and for i>n e 7 it completes the classification of permutation patterns by settling all remaining cases in i>S7.