4 papers
Quantizing Pythagorean triples
Hugo Mathevet, Sophie Morier-Genoud, Valentin Ovsienko
We introduce a -deformation of the Pythagoras equation , which is a polynomial version of it different from the standard one. We construct a polynomial analogue…
On -deformed Markov numbers. Cohn matrices and perfect matchings with weighted edges
Sam Evans, Perrine Jouteur, Sophie Morier-Genoud +1
We consider a natural -deformation of the classical Markov numbers. This -deformation is closely related to -deformed rational numbers recently introduced by two of us. Bo…
-deformed rationals and irrationals
Sophie Morier-Genoud, Valentin Ovsienko
The concept of -deformation, or ``-analogue'' arises in many areas of mathematics. In algebra and representation theory, it is the origin of quantum groups; -deformations…
On -deformed cubic equations: the quantum heptagon and nonagon
Valentin Ovsienko, Alexey Ustinov
The recent notion of -deformed irrational numbers is characterized by the invariance with respect to the action of the modular group $\PSL(2,\Z)$, or equivalently under the Bura…