Meanders in a Cayley graph
Combinatorics
2007-05-23 v1 Group Theory
Geometric Topology
Abstract
A meander of order n is a simple closed curve in the plane which intersects a horizontal line transversely at 2n points. (Meanders which differ by an isotopy of the line and plane are considered equivalent.) Let Gamma_n be the Cayley graph of the symmetric group S_n as generated by all (n choose 2) transpositions. Let Lambda_n be any interval of maximal length in Gamma_n; this graph is the Hasse diagram of the lattice of noncrossing partitions. The meanders of order n are in one-to-one correspondence with ordered pairs of maximally separated vertices of Lambda_n.
Keywords
Cite
@article{arxiv.math/0606170,
title = {Meanders in a Cayley graph},
author = {H. Tracy Hall},
journal= {arXiv preprint arXiv:math/0606170},
year = {2007}
}