Tiling bijections between paths and Brauer diagrams

Details Tiling bijections between paths and Brauer diagrams Tiling bijections between paths and Brauer diagrams

2009-06-04

arxiv.org/abs/0906.0912v2

Journal of Algebraic Combinatorics (2011) 33, no. 3, 427-453

Mathematics

Combinatorics

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

Scientific paper

10.1007/s10801-010-0252-6

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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