$q$-DEFORMED RATIONALS AND $q$-CONTINUED FRACTIONS
Abstrak
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 identity 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.
Topik & Kata Kunci
Penulis (2)
S. Morier-Genoud
V. Ovsienko
Akses Cepat
- Tahun Terbit
- 2018
- Bahasa
- en
- Total Sitasi
- 74×
- Sumber Database
- Semantic Scholar
- DOI
- 10.1017/fms.2020.9
- Akses
- Open Access ✓