Journal of Algebraic Combinatorics

, Volume 33, Issue 3, pp 427–453

Tiling bijections between paths and Brauer diagrams

Article

DOI: 10.1007/s10801-010-0252-6

Cite this article as:
Marsh, R.J. & Martin, P. J Algebr Comb (2011) 33: 427. doi:10.1007/s10801-010-0252-6

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.

Keywords

Brauer algebra Temperley–Lieb diagram Pipe dream Dyck path Overhang path Double-factorial combinatorics 

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of MathematicsUniversity of LeedsLeedsUK

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