Geodesic
Euler characteristic of the truncated order complex of generalized noncrossing partitions
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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The purpose of this paper 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.
DOI : 10.37236/232
Classification : 05A10, 05A15, 05A18
Mots-clés : root systems, reflection groups, Coxeter groups, generalized non-crossing partitions, chain enumeration, Euler characteristics, Chu-Vandermonde summation 
@article{10_37236_232,
     author = {D. Armstrong and C. Krattenthaler},
     title = {Euler characteristic of the truncated order complex of generalized noncrossing partitions},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/232},
     zbl = {1285.05175},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/232/}
}
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D. Armstrong; C. Krattenthaler. Euler characteristic of the truncated order complex of generalized noncrossing partitions. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/232

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