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\(q\)-deformed rationals and \(q\)-continued fractions

By Sophie Morier-Genoud and Valentin Ovsienko
We introduce a notion of \(q\)-deformed rational numbers and \(q\)-deformed continued fractions. A \(q\)-deformed rational is encoded by a triangulation of a polygon and can be computed recursively. The recursive formula is analogous to the \(q\)-deformed Pascal identitiy for the Gaussian binomial coefficients, but the Pascal triangle is replaced by... Show more
June 17, 2019
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