Article Dans Une Revue
Forum of Mathematics, Sigma
Année : 2020
Résumé
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 the Farey graph. The coefficients of the polynomials defining the q-rational count quiver subrepresentations of the maximal indecomposable representation of the graph dual to the triangulation. Several other properties, such as total positivity properties, q-deformation of the Farey graph, matrix presentations and q-continuants are given, as well as a relation to the Jones polynomial of rational knots.
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https://hal.science/hal-02270545
Soumis le : lundi 26 août 2019-02:05:05
Dernière modification le : mercredi 15 mai 2024-11:24:57
Dates et versions
- HAL Id : hal-02270545 , version 1
- DOI : 10.1017/fms.2020.9
Citer
Sophie Morier-Genoud, Valentin Ovsienko. q-DEFORMED RATIONALS AND q-CONTINUED FRACTIONS. Forum of Mathematics, Sigma, 2020, 8, pp.e13. ⟨10.1017/fms.2020.9⟩. ⟨hal-02270545⟩
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