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A Sturmian sequence related to the uniqueness conjecture for Markoff numbers
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Bugeaud, Yann, Reutenauer, Christophe and Siksek, Samir. (2009) A Sturmian sequence related to the uniqueness conjecture for Markoff numbers. Theoretical Computer Science, Vol.410 (No.30-32). pp. 2864-2869. ISSN 0304-3975
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Official URL: http://dx.doi.org/10.1016/j.tcs.2009.02.005
Abstract
Sturmian sequences appear in the work of Markoff on approximations of real numbers and minima of quadratic functions. In particular, Christoffel words, or equivalently pairs of relatively prime nonnegative integers, parametrize the Markoff numbers. It was asked by Frobenius if this parametrization is injective. We answer this conjecture for a particular subclass of these numbers, and show that a special Sturmian sequence of irrational slope determines the order of the Markoff numbers in this subclass. (C) 2009 Elsevier B.V. All rights reserved.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Theoretical Computer Science |
| Publisher: | Elsevier Science BV |
| ISSN: | 0304-3975 |
| Date: | 20 August 2009 |
| Volume: | Vol.410 |
| Number: | No.30-32 |
| Number of Pages: | 6 |
| Page Range: | pp. 2864-2869 |
| Identification Number: | 10.1016/j.tcs.2009.02.005 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/17492 |
Data sourced from Thomson Reuters' Web of Knowledge
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