{
  "abstract": "We give an elementary, straightforward proof of Ovenhouse's interpretation of the denominator and the numerator of a (right) q-deformed rational in terms of weighted lattice paths on a \"snake graph\", and we give an analogous result for the left q-deformed rational introduced by Bapat, Becker, and Licata. The key ingredient is a simple formula for the q-deformation of the matrix of the composition of two homographies of the form z → a + 1/z.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09953",
  "author_total": 1,
  "authors": [
    {
      "name": "Jérôme Germoni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ce9qee10kcczm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09953",
  "fulltext_url": null,
  "id": "ce9qee10kcczm",
  "issns": [],
  "landing_url": "https://hal.science/hal-05781778v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-co"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7220903568",
  "pdf_url": "https://hal.science/hal-05781778/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ce9qee10kcczm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:49Z",
      "native_id": "hal-05781778",
      "source": "hal",
      "url": "https://hal.science/hal-05781778v1"
    },
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09953",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09953"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Lattice paths on snake graphs for q-deformed rationals",
  "title_text": "Lattice paths on snake graphs for q-deformed rationals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/ce9qee10kcczm",
  "venue": "HAL",
  "versions": []
}