Publication at Faculty of Mathematics and Physics |

2023

An inversion sequence of length n is a sequence of integers e = e1...en which satisfies for each i in [n] = {1, 2, ... , n} the inequality 0 <= ei < i. For a set of patterns P, we let In(P) denote the set of inversion sequences of length n that avoid all the patterns from P.

We say that two sets of patterns P and Q are IWilf-equivalent if |In(P)| = |In(Q)| for every n. In this paper, we show that the number of I-Wilf-equivalence classes among triples of length-3 patterns is 137, 138 or 139.

In particular, to show that this number is exactly 137, it remains to prove {101, 102, 110} is IWilf equivalent to {021, 100, 101}, and {100, 110, 201} is IWilf equivalent to {100, 120, 210}.