Non-crossing partitions for classical reflection groups

Non-crossing partitions for classical reflection groups

We introduce analogues of the lattice of non-crossing set partitions for the classical reeection groups of type B and D. The type B analogues ((rst considered by Montenegro in a diierent guise) turn out to be as well-behaved as the original non-crossing set partitions, and the type D analogues almost as well-behaved. In both cases, they are EL-labellable ranked lattices with symmetric chain dec...

Non-crossing partitions for arbitrary Coxeter groups

Bijections between noncrossing and nonnesting partitions for classical reflection groups

We present type preserving bijections between noncrossing and nonnesting partitions for all classical reflection groups, answering a question of Athanasiadis and Reiner. The bijections for the abstract Coxeter types B, C and D are new in the literature. To find them we define, for every type, sets of statistics that are in bijection with noncrossing and nonnesting partitions, and this correspon...

On Noncrossing and Nonnesting Partitions for Classical Reflection Groups

The number of noncrossing partitions of {1, 2, . . . , n} with fixed block sizes has a simple closed form, given by Kreweras, and coincides with the corresponding number for nonnesting partitions. We show that a similar statement is true for the analogues of such partitions for root systems B and C, defined recently by Reiner in the noncrossing case and Postnikov in the nonnesting case. Some of...

Cyclic Sieving for Generalised Non–Crossing Partitions Associated to Complex Reflection Groups of Exceptional Type

We present the proof of the cyclic sieving conjectures for generalised non-crossing partitions associated to well-generated complex reflection groups due to Armstrong, respectively to Bessis and Reiner, for the 26 exceptional well-generated complex reflection groups. The computational details are provided in the manuscript “Cyclic sieving for generalised non-crossing partitions associated to co...