6 papers
The -deformed cross-ratio: modular invariants and Coxeter friezes
Valentin Ovsienko
We introduce and study a scalar -deformation of the cross-ratio on . Our construction is based on the notion of -deformed rational numbers due to Mori…
Coefficients of -real numbers: their combinatorial meaning and growth
Pavel Etingof, Valentin Ovsienko
A -deformed real number, or ``-real'', was defined by Morier-Genoud and the second author. When such that , the -analogue is a power serie…
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…