Emmanuel Pedon

collaborators

3 papers

math.CO2026

Analytical properties of $q$ -metallic numbers

Emmanuel Pedon

For an integer $n \geq 1$ , consider the $n$ -th metallic number $I ¨ _{n} = \frac{n + n ^{2} + 4}{2}$ (e.g. $I ¨ _{1}$ is the golden number) and denote by $[I ¨ _{n}]_{q}$ its $q$ -deformation in the…

math.NT2026

Hankel continued fractions and Hankel determinants for $q$ -deformed metallic numbers

Guo-Niu Han, Emmanuel Pedon

Fix $n$ a positive integer. Take the $n$ -th metallic number $I ¨ _{n} = \frac{n + n ^{2} + 4}{2}$ (e.g. $I ¨ _{1}$ is the golden number) and let $I^¦_{n} (q)$ be its $q$ -deformation in the sense…

math.CO2024

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…

Analytical properties of q-metallic numbers

Hankel continued fractions and Hankel determinants for q-deformed metallic numbers

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

Analytical properties of $q$ -metallic numbers

Hankel continued fractions and Hankel determinants for $q$ -deformed metallic numbers

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