A new class of multiset Wilf equivalent pairs

A New Class of Wilf-Equivalent Permutations

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, (n −1, n −2, n, τ ) ∼ (n −2, n, n −1, τ ) for any τ ∈ Sn−3. In particular, at level n = 6, this result includes the only missing equivalence (546213) ∼ (465213), and for n = 7 it compl...

An infinite family of inv-Wilf-equivalent permutation pairs

Operators of Equivalent Sorting Power and Related Wilf-equivalences

We study sorting operators A on permutations that are obtained composing Knuth’s stack sorting operator S and the reversal operator R, as many times as desired. For any such operator A, we provide a size-preserving bijection between the set of permutations sorted by S ◦ A and the set of those sorted by S ◦ R ◦ A, proving that these sets are enumerated by the same sequence, but also that many cl...

A New Class of Banach Sequence Spaces

Wilf Classes of Pairs of Permutations of Length 4

Sn(π1, π2, . . . , πr) denotes the set of permutations of length n that have no subsequence with the same order relations as any of the πi. In this paper we show that |Sn(1342, 2143)| = |Sn(3142, 2341)| and |Sn(1342, 3124)| = |Sn(1243, 2134)|. These two facts complete the classification of Wilf-equivalence classes for pairs of permutations of length four. In both instances we exhibit bijections...