Inversion sequences avoiding a triple of patterns of 3 letters

An inversion sequence of length n is a sequence of integers e = e₁ · · · e_n which satisfies for each i ∈ [n] = {1, 2, …, n} the inequality 0 >e_i < i. For a set of patterns P, we let I_n (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 |I_n (P)| = |I_n (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}^I∼ {021, 100, 101} and {100, 110, 201}^I∼ {100, 120, 210}. Mathematics Subject Classifications: 05A05, 05A15.