Restricted ascent sequences and Catalan
numbers
In this paper, we identify all members of the (4,4)-Wilf equivalence class for ascent sequences corresponding to the Catalan number . This extends recent work concerning avoidance of a single pattern and provides apparently new combinatorial interpretations for . In several cases, the subset of the class consisting of those members having exactly m ascents is given by the Narayana number . We conclude by considering a further refinement in the case of avoiding 021.
