Meander Determinants

Abstract

We prove a determinantal formula for quantities related to the problem of enumeration of (semi-) meanders, namely the topologically inequivalent planar configurations of non-self-intersecting loops crossing a given (half-) line through a given number of points. This is done by the explicit Gram-Schmidt orthogonalization of certain bases of subspaces of the Temperley-Lieb algebra.

arXiv commentTeX using harvmac.tex and epsf.tex, 64 pages (l-mode), 79 figures