Presentation of the Motzkin Monoid
| Autor: | Posner, Eliezer, Hatch, Kris, Ly, Megan |
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| Rok vydání: | 2013 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 24 pages, completed as undergraduates in the Research Experience for Undergraduates program at UC Santa Barbara |
| Databáze: | arXiv |
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