# L'INTERPRÉTATION MATRICIELLE DE LA THÉORIE DE MARKOFF CLASSIQUE

```@article{Perrine2002LINTERPRTATIONMD,
title={L'INTERPR{\'E}TATION MATRICIELLE DE LA TH{\'E}ORIE DE MARKOFF CLASSIQUE},
author={Serge Perrine},
journal={International Journal of Mathematics and Mathematical Sciences},
year={2002},
volume={32},
pages={193-262}
}```
• S. Perrine
• Published 2002
• Mathematics
• International Journal of Mathematics and Mathematical Sciences
On explicite l'approche de Cohn (1955) de la theorie de Markoff. On montre en particulier comment l'arbre complet des solutions de l'equation diophantienne associee apparasit comme quotient du groupe GL (2,ℤ) des matrices 2×2 a coefficients entiers et de determinant ±1 par un sous-groupe diedral D6 a 12 elements. Differents developpements intermediaires sont faits autour du groupe Aut (F 2)des automorphismes du groupe libre engendre par deux elements F 2.
Modified Hypergeometric Equations Arising from the Markoff Theory
• Mathematics
• 2003
After recalling what the Markoff theory is, this article summarizes some links which exist with the group GL(2, Z) of 2 × 2 matrices with integer coefficients and determinant ±1 and with its
From Frobenius to Riedel: analysis of the solutions of the Markoff equation
The main task is to identify the tree dealt with by Riedel, to generalize his formalization to his whole tree, modifying when necessary his definitions, and to give some corrections.
Markoff Equation and Nilpotent Matrices
A triple (a,b,c) of positive integers is called a Markoff triple iff it satisfies the diophantine equation a2 + b2 + c2 = abc . Recasting the Markoff tree, whose vertices are Markoff triples, in the
On the Markoff Equation
A triple (a, b, c) of positive integers is called a Markoff triple iff it satisfies the Diophantine equation a2+b2+c2=abc . Recasting the Markoff tree, whose vertices are Markoff triples, in the
Christoffel Words and Markoff Triples
Abstract We construct a bijection between Markoff triples and Christoffel words.