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- W2952823949 abstract "Let $Phi$ be a finite root system of rank $n$ and let $m$ be a nonnegative integer. The generalized cluster complex $Delta^m (Phi)$ was introduced by S. Fomin and N. Reading. It was conjectured by these authors that $Delta^m (Phi)$ is shellable and by V. Reiner that it is $(m+1)$-Cohen-Macaulay, in the sense of Baclawski. These statements are proved in this paper. Analogous statements are shown to hold for the positive part $Delta^m_+ (Phi)$ of $Delta^m (Phi)$. An explicit homotopy equivalence is given between $Delta^m_+ (Phi)$ and the poset of generalized noncrossing partitions, associated to the pair $(Phi, m)$ by D. Armstrong." @default.
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- W2952823949 date "2006-06-01" @default.
- W2952823949 modified "2023-09-27" @default.
- W2952823949 title "Shellability and higher Cohen-Macaulay connectivity of generalized cluster complexes" @default.
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