Ascent sequences avoiding a triple of length-3 patterns

An ascent sequence is a sequence a₁ a₂ · · · a_n consisting of non-negative integers satisfying a₁ = 0 and for 1 < i ≤ n, a_i ≤ asc(a₁ a₂ · · · a_i−1 )+1, where asc(a₁ a₂ · · · a_k ) is the number of ascents in the sequence a₁ a₂ · · · a_k . We say that two sets of patterns B and C are A-Wilf-equivalent if the number of ascent sequences of length n that avoid B equals the number of ascent sequences of length n that avoid C, for all n ≥ 0. In this paper, we show that the number of A-Wilf-equivalences among triples of length-3 patterns is 62. The main tool is generating trees; bijective methods are also sometimes used. One case is of particular interest: ascent sequences avoiding the 3 patterns 100, 201 and 210 are easy to characterize, but it seems remarkably involved to show that, like 021-avoiding ascent sequences, they are counted by the Catalan numbers.