On the (co)homology of the poset of weighted partitions

We consider the poset of weighted partitions \Pi _n^w provide a generalization of the lattice \Pi _n. In particular, we prove these intervals are EL-shellable, we show that the Möbius invariant of each maximal interval is given up to sign by the number of rooted trees on node set \{1,2,\dots ,n\} \m...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2016-10, Vol.368 (10), p.6779-6818
Main Authors: González D’León, Rafael S., Wachs, Michelle L.
Format: Article
Language:English
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Summary:We consider the poset of weighted partitions \Pi _n^w provide a generalization of the lattice \Pi _n. In particular, we prove these intervals are EL-shellable, we show that the Möbius invariant of each maximal interval is given up to sign by the number of rooted trees on node set \{1,2,\dots ,n\} \mathfrak{S}_n has a nice factorization analogous to that of .
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/6483