On the Markov numbers: fixed numerator, denominator, and sum conjectures

DOI10.1016/j.aam.2021.102227zbMath1493.11068arXiv2010.10335OpenAlexW3165199064WikidataQ123264044 ScholiaQ123264044MaRDI QIDQ2048376

Laurent Vuillon, Clément Lagisquet, Sébastien Tavenas, Edita Pelantová

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/2010.10335

zbMATH Keywords

Markov numbersfixed denominator conjecturefixed numerator conjecturefixed sum conjecture

Mathematics Subject Classification ID

Combinatorics on words (68R15) Cubic and quartic Diophantine equations (11D25) Markov and Lagrange spectra and generalizations (11J06) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (3)

Boundary slopes for the Markov ordering on relatively prime pairs ⋮ Unnamed Item ⋮ On the ordering of the Markov numbers

Cites Work

• Unnamed Item
• Continued fractions and orderings on the Markov numbers
• Continued fractions and the Markoff tree
• Approach to Markoff's minimal forms through modular functions
• Markov's Theorem and 100 Years of the Uniqueness Conjecture
• The Modular Surface and Continued Fractions
• Combinatorics on Words
• Palindromic Closures and Thue-Morse Substitution for Markoff Numbers

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