Chain enumeration of $k$-divisible noncrossing partitions of classical types

Details Chain enumeration of $k$-divisible noncrossing partitions of classical types Chain enumeration of $k$-divisible noncrossing partitions of classical types

2009-08-18

arxiv.org/abs/0908.2641v4

J. Combin. Theory Ser. A 118 (2011) 879-898

Mathematics

Combinatorics

23 pages, 9 figures, final version

Scientific paper

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 M{\"u}ller. We also prove Armstrong's conjecture on the zeta polynomial of the poset of $k$-divisible noncrossing partitions of type $A$ invariant under a $180^\circ$ rotation in the cyclic representation.

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