Ron M. Adin, Yuval Roichman
Published 2012-01-23, updated 2013-12-23Version 3
A weak order on the set of maximal chains of the non-crossing partition lattice is introduced and studied. A $0$-Hecke algebra action is used to compute the radius of the graph on these chains in which two chains are adjacent if they differ in exactly one element.
Comments: 27 pages, 2 figures. Extensive changes, including addition of a section on alternating non-crossing trees and a section with open problems
A conjecture on descents, inversions and the weak order
The Sperner property for $132$-avoiding intervals in the weak order
Homomorphism Complexes and Maximal Chains in Graded Posets
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