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Chain enumeration of k-divisible noncrossing partitions of classical types

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 Müller. We also prove Armstrong's conjecture on the zeta polynomial of the poset of k-divisible noncrossing partitions of type A invariant under the 180° rotation in the cyclic representation.
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Jang Soo Kim. Chain enumeration of k-divisible noncrossing partitions of classical types. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.809-820, ⟨10.46298/dmtcs.2813⟩. ⟨hal-01186241⟩

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