Wilf classes for weak ascent sequences avoiding a pair or triple of length-3 patterns

A weak ascent sequence is a word π=π₁π₂⋯π_n over the set of nonnegative integers such that π₁=0 and π_i≤1+weak_asc(π₁π₂⋯π_i−1) for i=2,…,n, where weak_asc(π₁π₂⋯π_m) is the number of weak ascents in the word π₁π₂⋯π_m, that is, the number of two-entry factors π_jπ_j+1 such that π_j≤π_j+1. Here we obtain some enumerative results for weak ascent sequences avoiding a set of two or three 3-letter patterns, leading to a conjecture for the number of Wilf equivalence classes for weak ascent sequences avoiding a pair (respectively, triple) of 3-letter patterns. The main tool is the use of generating trees. Some cases are treated using bijective methods.