Generalized Non-Crossing Partitions and Buildings
نویسندگان
چکیده
For any finite Coxeter group W of rank n we show that the order complex of the lattice of non-crossing partitions NC(W ) embeds as a chamber subcomplex into a spherical building of type An−1. We use this to give a new proof of the fact that the non-crossing partition lattice in type An is supersolvable for all n. Moreover, we show that in case Bn, this is only the case if n < 4. We also obtain a lower bound on the radius of the Hurwitz graph H(W ) in all types and re-prove that in type An the radius is ( n 2 ) .
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 25 شماره
صفحات -
تاریخ انتشار 2018