Tiling bijections between paths and Brauer diagrams

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.

The final publication is available at www.springerlink.com. 30 pages, 34 figures

References in corpus (2)

• A geometric characterisation of the blocks of the Brauer algebra
• Pascal arrays: counting Catalan sets

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