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 $x\in \mathbb{R}$ such that $x\ge 0$, the $q$-analogue $[x{]}_q$ is a power serie…