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Meanders and the Temperley-Lieb algebra

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Abstract

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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Correspondence to P. Di Francesco, O. Golinelli or E. Guitter.

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Francesco, P.D., Golinelli, O. & Guitter, E. Meanders and the Temperley-Lieb algebra. Commun. Math. Phys. 186, 1–59 (1997). https://doi.org/10.1007/BF02885671

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  • DOI: https://doi.org/10.1007/BF02885671

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