ASCENT SEQUENCES AND WEAK ASCENT SEQUENCES AVOIDING A QUADRUPLE OF LENGTH-3 PATTERNS

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 all the patterns in B equals the number of ascent sequences of length n that avoid all the patterns in C, for all n ≥ 0. Similarly, WA-Wilf-equivalence refers to weak ascent sequences. Here, we show that the number of A-Wilf-equivalence classes among quadruples of length-3 patterns is 74 and the number of WA-Wilf-equivalence classes among quadruples of length-3 patterns is either 228 or 229. The main tool is generating trees; bijective methods are also sometimes used.