{"paper":{"title":"On $q$-deformed Markov numbers. Cohn matrices and perfect matchings with weighted edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Perrine Jouteur, Sam Evans, Sophie Morier-Genoud, Valentin Ovsienko","submitted_at":"2025-07-25T09:06:15Z","abstract_excerpt":"We consider a natural $q$-deformation of the classical Markov numbers. This $q$-deformation is closely related to $q$-deformed rational numbers recently introduced by two of us. Both notions, those of $q$-rationals and $q$-Markov numbers, are based on invariance with respect to the action of the modular group $mathrm{PSL}(2,\\mathbb{Z})$. We prove that every Markov number has a unique $q$-deformation, which is a monic unimodal palindromic Laurent polynomial with positive integer coefficients. The $q$-Markov numbers can be calculated in terms of the traces of $q$-deformed Cohn matrices, and we s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19080","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.19080/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}