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

Jang Soo Kim

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

Combinatorics 2011-08-30 v4

Authors: Jang Soo Kim

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{\"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.

Keywords

noncrossing partitions chain enumeration zeta polynomial classical types combinatorial proof

Cite

@article{arxiv.0908.2641,
  title  = {Chain enumeration of $k$-divisible noncrossing partitions of classical types},
  author = {Jang Soo Kim},
  journal= {arXiv preprint arXiv:0908.2641},
  year   = {2011}
}

Comments

23 pages, 9 figures, final version

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