\(q\)-deformations in the modular group and of the real quadratic irrational numbers

DOI10.1016/j.aam.2021.102223zbMath1480.11012arXiv2101.02953OpenAlexW3165369210MaRDI QIDQ2048370

Ludivine Leclere, Sophie Morier-Genoud

Publication date: 5 August 2021

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.02953

zbMATH Keywords

\(q\)-analoguesmodular groupcontinued fractionsunimodalitycontinuantsquadratic irrationalspalindromic polynomials

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Structure of modular groups and generalizations; arithmetic groups (11F06) Continued fractions (11A55)

Related Items (9)

The $q$-analog of the Markoff injectivity conjecture over the language of a balanced sequence ⋮ On radiuses of convergence of \(q\)-metallic numbers and related \(q\)-rational numbers ⋮ \(q\)-rationals and finite Schubert varieties ⋮ Ideal lattices of fence posets and rank unimodality ⋮ A \(q\)-analog of the Markoff injectivity conjecture holds ⋮ q-deformed rational numbers and the 2-Calabi–Yau category of type ⋮ \(q\)-rational and \(q\)-real binomial coefficients ⋮ Quantum continuants, quantum rotundus and triangulations of annuli ⋮ Rank polynomials of fence posets are unimodal

Cites Work

• Hilbert modular surfaces
• Farey boat: continued fractions and triangulations, modular group and polygon dissections
• From Christoffel Words to Markoff Numbers
• -DEFORMED RATIONALS AND -CONTINUED FRACTIONS
• A bridge between Conway–Coxeter friezes and rational tangles through the Kauffman bracket polynomials
• On a rank-unimodality conjecture of Morier-Genoud and Ovsienko
• Unnamed Item

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