Palindromization and construction of Markoff triples
| Autor: | Antoine Abram, Christophe Reutenauer, Mélodie Lapointe |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Christoffel symbols
General Computer Science Diophantine equation 010102 general mathematics Palindrome 0102 computer and information sciences 01 natural sciences Theoretical Computer Science Combinatorics Set (abstract data type) 010201 computation theory & mathematics Free monoid Bijection 0101 mathematics Mathematics |
| Zdroj: | Theoretical Computer Science. 809:21-29 |
| ISSN: | 0304-3975 |
| DOI: | 10.1016/j.tcs.2019.10.048 |
| Popis: | The Markoff equation is the Diophantine equation x 2 + y 2 + z 2 = 3 x y z . A solution is called a Markoff triple. We give a bijection between the free monoid on two letters and the set of Markoff triples, using the palindromization map of Aldo de Luca. In our construction, special Christoffel words appear, whose lengths are Markoff numbers; we study their standard and palindromic factorizations, and show that they are self-dual. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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