Valentin Ovsienko

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20242026

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math.DG2026

The $q$ -deformed cross-ratio: modular invariants and Coxeter friezes

Valentin Ovsienko

We introduce and study a scalar $q$ -deformation of the cross-ratio on $P^{1} (Q)$ . Our construction is based on the notion of $q$ -deformed rational numbers due to Mori…

math.CO2026

Coefficients of $q$ -real numbers: their combinatorial meaning and growth

Pavel Etingof, Valentin Ovsienko

A $q$ -deformed real number, or `` $q$ -real'', was defined by Morier-Genoud and the second author. When $x \in R$ such that $x \geq 0$ , the $q$ -analogue $[x]_{q}$ is a power serie…

math.CO2026

Quantizing Pythagorean triples

Hugo Mathevet, Sophie Morier-Genoud, Valentin Ovsienko

We introduce a $q$ -deformation of the Pythagoras equation $a^{2} + b^{2} = c^{2}$ , which is a polynomial version of it different from the standard one. We construct a polynomial analogue…

The q-deformed cross-ratio: modular invariants and Coxeter friezes

Coefficients of q-real numbers: their combinatorial meaning and growth

Quantizing Pythagorean triples

The $q$ -deformed cross-ratio: modular invariants and Coxeter friezes

Coefficients of $q$ -real numbers: their combinatorial meaning and growth