Continued fractions for $q$-deformed real numbers, $\{-1,0,1\}$-Hankel determinants, and Somos-Gale-Robinson sequences

Valentin Ovsienko, Emmanuel Pedon

$q$-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 ne…