Euler characteristic of the truncated order complex of generalized noncrossing partitions

Details Euler characteristic of the truncated order complex of generalized noncrossing partitions Euler characteristic of the truncated order complex of generalized noncrossing partitions

2009-05-02

arxiv.org/abs/0905.0205v1

Electronic J. Combin. 16(1) (2009), Article #R143, 10 pp.

Mathematics

Combinatorics

8 pages, AmS-LaTeX

Scientific paper

The purpose of this note is to complete the study, begun in the first author's PhD thesis, of the topology of the poset of generalized noncrossing partitions associated to real reflection groups. In particular, we calculate the Euler characteristic of this poset with the maximal and minimal elements deleted. As we show, the result on the Euler characteristic extends to generalized noncrossing partitions associated to well-generated complex reflection groups.

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