Meanders and the Temperley-Lieb algebra
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- Francesco, P.D., Golinelli, O. & Guitter, E. Commun. Math. Phys. (1997) 186: 1. doi:10.1007/BF02885671
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The statistics of meanders is studied in connection with the Temperley-Lieb algebra. Each (multi-component) meander corresponds to a pair of reduced elements of the algebra. The assignment of a weightq per connected component of meander translates into a bilinear form on the algebra, with a Gram matrix encoding the fine structure of meander numbers. Here, we calculate the associated Gram determinant as a function ofq, and make use of the orthogonalization process to derive alternative expressions for meander numbers as sums over correlated random walks.
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