Abstract
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.
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This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/G007497/1].
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Marsh, B.R., Martin, P. Tiling bijections between paths and Brauer diagrams. J Algebr Comb 33, 427–453 (2011). https://doi.org/10.1007/s10801-010-0252-6
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DOI: https://doi.org/10.1007/s10801-010-0252-6