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

Jang Soo Kim

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arXiv · 0908.2641

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

Jang Soo Kim

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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 M{ü}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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BibTeX RIS

Jang Soo Kim. 2011-08-29. Chain enumeration of $k$-divisible noncrossing partitions of classical types. https://arxiv.org/abs/0908.2641

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