Inversion sequences and signed permutations
Toufik Mansour, Amir Safadi · Discrete Mathematics Letters · 2024
A signed inversion sequence of length n is a sequence of integers e = e1 • • • en, where ei+1 ∈ {0, 0, 1, 1, . . ., i, ī } for every i ∈ {0, 1, . . ., n -1}.For a set of signed patterns B, let Īn(B) be the set of signed inversion sequences of length n that avoid all the signed patterns from B. We say that two sets of signed patterns B and C are Wilf-equivalent if | Īn(B)| = | Īn(C)| for every n ≥ 0. In this paper, by generating trees, we show that the number of Wilf-equivalences among singles of a length-2 signed pattern is 3 and the number of Wilf-equivalences among pairs of a length-2 signed patterns is 30.