45 citations · 146 across the 27 of their papers we have counts for
34 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…
Burau representation of braid groups and -rationals
Sophie Morier-Genoud, Valentin Ovsienko, Alexander Veselov
We establish a link between the new theory of -deformed rational numbers and the classical Burau representation of the braid group . We apply this link to the open…
Quantum continuants, quantum rotundus and triangulations of annuli
Ludivine Leclere, Sophie Morier-Genoud
We give enumerative interpretations of the polynomials arising as numerators and denominators of the -deformed rational numbers introduced by Morier-Genoud and Ovsienko. The con…
On radius of convergence of -deformed real numbers
Ludivine Leclere, Sophie Morier-Genoud, Valentin Ovsienko +1
We study analytic properties of ``-deformed real numbers'', a notion recently introduced by two of us. A -deformed positive real number is a power series with integer coeffic…