Tiling bijections between paths and Brauer diagrams
Abstract
There is a natural bijection between Dyck paths and basis diagrams of the TemperleyLieb algebra defined via tiling. Overhang paths are certain generalisations of Dyck paths allowing more general steps but restricted to a rectangle in the twodimensional 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2009
 arXiv:
 arXiv:0906.0912
 Bibcode:
 2009arXiv0906.0912M
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Representation Theory;
 05A10;
 16S99
 EPrint:
 The final publication is available at www.springerlink.com. 30 pages, 34 figures