Wilf Classes for Weak Ascent Sequences Avoiding a Pair
or Triple of Length-3 Patterns
A \emph{weak ascent sequence} is a word $\pi=\pi_1\pi_2\cdots\pi_n$ over the
set of nonnegative integers such that $\pi_1=0$ and $\pi_i\leq1+\wasc(\pi_1\pi_2\cdots\pi_{i-1})$ for $i=2, \dots, n$, where $\wasc(\pi_1\pi_2\cdots\pi_m)$ is the numbers of \emph{weak ascents} in the
word $\pi_1\pi_2\cdots\pi_m$, that is, the number of positions $j$ such that $\pi_j\leq \pi_{j+1}$.
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, called $A$-Wilf equivalence classes, 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.
