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arXiv · 1301.4518

Presentation of the Motzkin Monoid

Eliezer Posner·Kris Hatch·Megan Ly
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Abstract

In 2010, Tom Halverson and Georgia Benkart introduced the Motzkin algebra, a generalization of the Temperley-Lieb algebra, whose elements are diagrams that can be multiplied by stacking one on top of the other. Halverson and Benkart gave a diagrammatic algorithm for decomposing any Motzkin diagram into diagrams of three subalgebras: the Right Planar Rook algebra, the Temperley-Lieb algebra, and the Left Planar Rook algebra. We first explore the Right and Left Planar Rook monoids, by finding presentations for these monoids by generators and relations, using a counting argument to prove that our relations suffice. We then turn to the newly-developed Motzkin monoid, where we describe Halverson's decomposition algorithm algebraically, find a presentation by generators and relations, and use a counting argument but with a much more sophisticated algorithm.

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BibTeXRIS

Eliezer Posner, Kris Hatch, Megan Ly. 2013-01-18. Presentation of the Motzkin Monoid. https://arxiv.org/abs/1301.4518

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