{
  "abstract": "Version Control Systems, like Git and Mercurial, represent the history of a project as a Directed Acyclic Graph, capturing divergences and merges throughout development. A widely adopted workflow, the feature branch workflow, imposes a particularly simple structure: a single main branch and features branches evolving in parallel without interfering with one another. This work presents an enumerative study of these Git graphs. We first establish a bijection between Git graphs and a simpler combinatorial class, which we term cyclariums, and derive their exact count at size n, namely \\( \\sum_{k=2}^n \\sum_{f = 1}^{k-1} {k \\brack f} { n - k - 1 \\choose k - f - 1} \\). Using a saddle-point method, we further show that this number is asymptotically equivalent to \\[ \\frac{e^{1/8}}{2} \\left(\\frac{n}{2e}\\right)^{\\frac n 2} \\exp\\left(\\frac 1 2 \\ln\\frac n 2 \\sqrt{\\frac n 2} + \\sqrt{2 n} + \\frac{(\\ln\\frac n 2)^2}{32} \\right) \\left(\\frac n 2\\right)^{-3/8}. \\] Additionally, we analyze the limit laws of key parameters. Finally, we address random generation by designing both a uniform sampler and a Boltzmann sampler for these graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37208",
  "author_total": 2,
  "authors": [
    {
      "name": "Julien Courtiel"
    },
    {
      "name": "Martin Pépin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bgt97kfgyxfpv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37208",
  "fulltext_url": null,
  "id": "bgt97kfgyxfpv",
  "issns": [],
  "landing_url": "https://hal.science/hal-05840557v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/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": "W7224129941",
  "pdf_url": "https://hal.science/hal-05840557/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bgt97kfgyxfpv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:02Z",
      "native_id": "hal-05840557",
      "source": "hal",
      "url": "https://hal.science/hal-05840557v1"
    },
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37208",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37208"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Counting and Sampling Git Graphs",
  "title_text": "Counting and Sampling Git Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/bgt97kfgyxfpv",
  "venue": "HAL",
  "versions": []
}