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 our tools come from the theory of hyperplane arrangements. Submitted: January 30, 1998; Accepted: September 10, 1998

• Type: Journal
• Year: 1998
• Where: COMBINATORICS
• Authors: Christos A. Athanasiadis
• Keywords: COMBINATORICS 1998, Corresponding Number, Nonnesting Partitions, Simple Closed Form