Tiling bijections between paths and Brauer diagrams

Bethany Marsh and Paul Martin
Arxiv ID: 0906.0912Last updated: 12/21/2020
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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