On maximal chains in the non-crossing partition lattice

Ron M. Adin; Yuval Roichman

On maximal chains in the non-crossing partition lattice

Combinatorics 2013-12-25 v3 Group Theory

Authors: Ron M. Adin , Yuval Roichman

Abstract

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.

Keywords

noncrossing partitions graph pebbling lattice theory

Cite

@article{arxiv.1201.4669,
  title  = {On maximal chains in the non-crossing partition lattice},
  author = {Ron M. Adin and Yuval Roichman},
  journal= {arXiv preprint arXiv:1201.4669},
  year   = {2013}
}

Comments

27 pages, 2 figures. Extensive changes, including addition of a section on alternating non-crossing trees and a section with open problems

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