Descents and des-Wilf equivalence of permutations avoiding certain nonclassical patterns

Abstract

A frequent topic in the study of pattern avoidance is identifying when two sets of patterns $\mathrm{\Pi },{\mathrm{\Pi }}^{\prime }$ are Wilf equivalent, that is, when $\left|{Av}_n\left(\mathrm{\Pi }\right)\right|=\left|{Av}_n\left({\mathrm{\Pi }}^{\prime }\right)\right|$ for all $n$. In recent work of Dokos et al. the notion of Wilf equivalence was refined to reflect when avoidance of classical patterns preserves certain statistics. We continue their work by examining des-Wilf equivalence when avoiding certain nonclassical patterns.