Enumerative and combinatorial properties of Dyck partitions

  • Authors:

  • Francesco Brenti

  • Affiliations:

  • Dipartimento di Matematica, Universitá di Roma "Tor Vergata," Via della Ricerca Scientifica, 1 00133 Rome, Italy

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2002

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Abstract

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 Young's lattice. As a consequence of our results, we obtain some new identities for these polynomials.