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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. (Update)
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0.7: Lattice Animals and Heaps of Dimers - Bousquet-Melou, Rechnitzer (Correct)
0.3: Upper and Lower Bounds for Kazhdan-Lusztig Polynomials - Brenti (Correct)
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BibTeX entry: (Update)
@misc{ brenti-enumerative,
author = "Francesco Brenti",
title = "Enumerative and Combinatorial Properties of Dyck Partitions",
url = "citeseer.ist.psu.edu/692992.html" }
Citations (may not include all citations):157 Advanced Combinatorics (context) - Comtet - 1974
73 Representations of Coxeter groups and Hecke algebras (context) - Kazhdan, Lusztig - 1979
50 Wadsworth and BrookCole (context) - Combinatorics, Wadsworth et al. - 1986
47 Cambridge Studies in Advanced Mathematics (context) - Stanley, Combinatorics - 1999
41 Re ection Groups and Coxeter Groups (context) - Humphreys - 1990
24 On some geometric aspects of Bruhat orderings (context) - Deodhar - 1987
20 Log-concave and unimodal sequences in Algebra (context) - Stanley - 1989
12 Log-concave and unimodal sequences in Algebra (context) - Brenti - 1994
6 Combinatorics of Coxeter Groups (context) - Bj, Brenti - 2001
5 Critical exponents from nonlinear functional equations for p.. (context) - Prellberg, Brak - 1995
4 Geometry of the Laplace operator (context) - Kazhdan, Lusztig et al. - 1980
3 Ane permutations of type (context) - Bj, Brenti - 1996
2 eration de polyominos convexes diriges (context) - Bousquet-M, Viennot et al. - 1992
2 and Dyck partitions (context) - Brenti, R-polynomials et al.
1 Ordering the ane symmetric group (context) - Lascoux
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