Inversion Sequences Avoiding a Triple of Patterns of 3 Letters
An inversion sequence of length n is a sequence of integers e = e_1, ..., e_n which satisfies for each i in [n] = {1, 2, ..., n} the inequalities 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 I-Wilf-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 between 137 and 139. In particular, to show this number is exactly 137, it remains to prove that {101, 102, 110} is I-Wilf-equivalent to {021, 100, 101} and {100, 110, 201} is I-Wilf-equivalent to {100, 120, 210}.
