Zobrazeno 1 - 10
of 186
pro vyhledávání: '"Ovsienko, Valentin"'
Autor:
Bonin, Nathan, Ovsienko, Valentin
Publikováno v:
Comptes Rendus. Mathématique, Vol 361, Iss G9, Pp 1483-1489 (2023)
We introduce an analogue of the classical Markov equation that involves dual numbers $a+\alpha \varepsilon $ with $\varepsilon ^2=0$. This equation characterizes the “shadow Markov numbers” recently considered by one of us. We show that this equa
Externí odkaz:
https://doaj.org/article/809d54dd228b4d56a1bc90bf4afeef65
Autor:
Ovsienko, Valentin, Ustinov, Alexey
The recent notion of $q$-deformed irrational numbers is characterized by the invariance with respect to the action of the modular group $\PSL(2,\Z)$, or equivalently under the Burau representation of the braid group~$B_3$. The theory of $q$-deformed
Externí odkaz:
http://arxiv.org/abs/2408.13670
Autor:
Ovsienko, Valentin, Pedon, Emmanuel
$q$-deformed real numbers are power series with integer coefficients. We study Stieltjes and Jacobi type continued fraction expansions of $q$-deformed real numbers and find many new examples of such continued fractions. We also investigate the corres
Externí odkaz:
http://arxiv.org/abs/2312.17009
We establish a link between the new theory of $q$-deformed rational numbers and the classical Burau representation of the braid group $\mathrm{B}_3$. We apply this link to the open problem of classification of faithful complex specializations of this
Externí odkaz:
http://arxiv.org/abs/2309.04240
Autor:
Bonin, Nathan, Ovsienko, Valentin
We introduce a superanalogue of the classical Markov equation. This equation characterizes the ``shadow Markov numbers'' recently considered by one of us. We show that this equation is characterized by invariance by cluster algebra mutations.
Co
Co
Externí odkaz:
http://arxiv.org/abs/2211.16087
Shadows of rationals and irrationals: supersymmetric continued fractions and the super modular group
Autor:
Conley, Charles H., Ovsienko, Valentin
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 integral ring with exactly two odd variables. In this case the even quantit
Externí odkaz:
http://arxiv.org/abs/2209.10426
Autor:
Ovsienko, Valentin, Pedon, Emmanuel
Publikováno v:
In Advances in Applied Mathematics January 2025 162
Autor:
Conley, Charles H, Ovsienko, Valentin
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, more difficult than enumerating the dissections themselves. Enumerat
Externí odkaz:
http://arxiv.org/abs/2202.00269