Restricted ascent sequences and Catalan numbers

Abstract

In this paper, we identify all members of the (4,4)-Wilf equivalence class for ascent sequences corresponding to the Catalan number Cn = 1 / n+1 (2n/n). This extends recent work concerning avoidance of a single pattern and provides apparently new combinatorial interpretations for Cn. In several cases, the subset of the class consisting of those members having exactly m ascents is given by the Narayana number Nn;m+1 = 1 / n (n/m+1)(n/m). We conclude by considering a further refinement in the case of avoiding 021.