Meanders in a Cayley graph
H. Tracy Hall
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 Gamman be the Cayley graph of the symmetric group Sn as generated by all (n choose 2) transpositions. Let Lambdan be any interval of maximal length in Gamman; 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 Lambdan.
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