On Noncrossing and Nonnesting Partitions for Classical Reflection Groups

Abstract

The number of noncrossing partitions of $\{1,2,\ldots,n\}$ 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 our tools come from the theory of hyperplane arrangements.