70 citations · 395 across the 55 of their papers we have counts for
60 papers
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…
Shadows of rationals and irrationals: supersymmetric continued fractions and the super modular group
Charles H. Conley, Valentin Ovsienko
This paper is an attempt to apply the tools of supergeometry to arithmetic. Supergeometric objects are defined over supercommutative rings of coefficients, and we consider an integ…
Counting quiddities of polygon dissections
Charles H Conley, Valentin Ovsienko
We formulate the following general problem. To the best of our knowledge, it is open and has not previously been considered. It seems (at least to us!) to be difficult; at any rate…
Shadow sequences of integers, from Fibonacci to Markov and back
Valentin Ovsienko
The following general idea looks crazy. What if another integer sequence follows each integer sequence like a shadow? I will demonstrate that this is indeed the case, perhaps not f…
On Ramanujan's cubic composition formula
Valentin Ovsienko
This is an elementary explanation of a cubic composition formula due to Ramanujan.
Quiddities of polygon dissections and the Conway-Coxeter frieze equation
Charles H. Conley, Valentin Ovsienko
We study a matrix equation arising naturally in the theory of Coxeter frieze patterns. It is formulated in terms of the generators of the group $\mathrm{PSL}(2,\mathbb…