Chain enumeration of k-divisible noncrossing partitions of classical types

Authors:
Jang Soo Kim
Affiliations:
LIAFA, Université Paris Diderot, 175 rue du Chevaleret, 75013 Paris, France
Venue:
Journal of Combinatorial Theory Series A
Year:
2011

Citing 2
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Abstract

We give combinatorial proofs of the formulas for the number of multichains in the k-divisible noncrossing partitions of classical types with certain conditions on the rank and the block size due to Krattenthaler and Muller. We also prove Armstrong's conjecture on the zeta polynomial of the poset of k-divisible noncrossing partitions of type A invariant under a 180^o rotation in the cyclic representation.