Enumerative and Combinatorial Properties of Dyck Partitions

The purpose of this paper is to study the combinatorial and enumerative properties of a new class of (skew) integer partitions. This class is closely related to Dyck paths and plays a fundamental role in the computation of certain Kazhdan–Lusztig polynomials of the symmetric group related to Youngʹs lattice. As a consequence of our results, we obtain some new identities for these polynomials.