Markov fractions and Cohn matrices

[2604.17401] Markov fractions and Cohn matrices Skip to main content Search Submit Donate Log in Mathematics > Number Theory arXiv:2604.17401 (math) [Submitted on 19 Apr 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Markov fractions and Cohn matrices Authors: A.P. Veselov View PDF HTML (experimental) Abstract: We show that the Markov fractions introduced recently by Springborn coincide with the index of the Cohn matrices defined by Aigner. This provides a simple concatenation rule for the corresponding continued fractions on the Conway topograph. We also discuss the $q$-deformation of Markov fractions in the sense of Morier-Genoud and Ovsienko, as well as their ``metallic" version motivated by the work of Spalding and the author. Comments: Extended version with $q$-deformed and "metallic" generalisations added Subjects: Number Theory (math.NT) MSC classes: 11A55, 11J06 Cite as: arXiv:2604.17401 [math.NT] (or arXiv:2604.17401v2 [math.NT] for this version) https://doi.org/10.48550/arXiv.2604.17401 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Alexander Veselov [ view email ] [v1] Sun, 19 Apr 2026 12:06:20 UTC (71 KB) [v2] Fri, 28 Aug 2026 09:57:51 UTC (77 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.NT < prev | next > new | recent | 2026-04 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Markov fractions and Cohn matrices#682651
• Quantum Estimation of Non-Hermitian Pseudospectra#1117345
• Kadison-Kastler Distance and Interior Angle for Masas: Connections with Entropy and Probabilistic Index#1142807
• Spectra of Non-Self-Adjoint Almost Mathieu Matrices and the Scottish Flag Operator#799412
• Spectra of Non-Self-Adjoint Almost Mathieu Matrices and the Scottish Flag Operator#797989