Geodesic
Tiling bijections between paths and Brauer diagrams
Journal of Algebraic Combinatorics, Tome 33 (2011) no. 3, pp. 427-453.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: There is a natural bijection between Dyck paths and basis diagrams of the Temperley-Lieb algebra defined via tiling. $Overhang$ paths are certain generalisations of Dyck paths allowing more general steps but restricted to a rectangle in the two-dimensional integer lattice. We show that there is a natural bijection, extending the above tiling construction, between overhang paths and basis diagrams of the Brauer algebra.
Keywords: keywords Brauer algebra, temperley-Lieb diagram, pipe dream, Dyck path, overhang path, double-factorial combinatorics 
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     author = {Marsh, Robert J. and Martin, Paul},
     title = {Tiling bijections between paths and {Brauer} diagrams},
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Marsh, Robert J.; Martin, Paul. Tiling bijections between paths and Brauer diagrams. Journal of Algebraic Combinatorics, Tome 33 (2011) no. 3, pp. 427-453. http://geodesic.mathdoc.fr/item/JAC_2011__33_3_a2/