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arXiv · 1509.06942

Symmetric Decompositions and the Strong Sperner Property for Noncrossing Partition Lattices

Henri Mühle
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Abstract

We prove that the noncrossing partition lattices associated with the complex reflection groups $G(d,d,n)$ for $d,n\geq 2$ admit symmetric decompositions into Boolean subposets. As a result, these lattices have the strong Sperner property and their rank-generating polynomials are symmetric, unimodal, and $γ$-nonnegative. We use computer computations to complete the proof that every noncrossing partition lattice associated with a well-generated complex reflection group is strongly Sperner, thus answering affirmatively a question raised by D. Armstrong.

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Henri Mühle. 2016-10-06. Symmetric Decompositions and the Strong Sperner Property for Noncrossing Partition Lattices. https://doi.org/10.1007/s10801-016-0723-5

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