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Communications in Algebra Volume 41, 2013 - Issue 3
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Original Articles

Christoffel Words and Markoff Triples: An Algebraic Approach

Alex Lasnier Département de Mathématiques, Université de Sherbrooke, Sherbrooke, Québec, CanadaCorrespondence[email protected]
Pages 1195-1216 | Received 06 Jun 2011, Published online: 13 Mar 2013
 
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Abstract

We introduce a family of modules, called Markoff modules, generated by a cluster-mutation-like iterative process. We show that these modules are combinatorially similar to Christoffel words. Furthermore, we construct a bijective map between the set of Markoff module triples and the set of proper Markoff triples. This allows us to interpret the uniqueness conjecture for Markoff numbers within an algebraic framework.

2012 Mathematics Subject Classification:

Notes

Communicated by D. Zacharia.

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