Enumerative properties of shifted-Dyck partitions

  • Authors:

  • Francesco Brenti

  • Affiliations:

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

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2010

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Abstract

We study the enumerative properties of a new class of (skew) shifted partitions. This class arises in the computation of certain parabolic Kazhdan-Lusztig polynomials and is closely related to ballot sequences. As consequences of our results, we obtain new identities for the parabolic Kazhdan-Lusztig polynomials of Hermitian symmetric pairs and for the ordinary Kazhdan-Lusztig polynomials of certain Weyl groups.