Emmanuel Pedon

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20232026

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math.CO2026

Analytical properties of $q$ -metallic numbers

Emmanuel Pedon

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

math.CO2023

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

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

Analytical properties of $q$ -metallic numbers

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