{
  "abstract": "Gaussian elimination with partial pivoting (GEPP) remains the most widely used solver for dense linear systems $A \\mathbf x = \\mathbf b$ for $A \\in \\mathbb C^{n\\times n}$. We study the permutation $π= π(A)$ that arises in the GEPP factorization $PA = LU$, encoded by the permutation matrix factor $P = P_π$. When the input matrix is random, so is $π$. For random scalar butterfly matrices of size $2^n$ (a recursively defined family originally introduced to eliminate the need for pivoting altogether), we give the exact GEPP factorization and fully classify the induced permutation as an element of a $2$-Sylow subgroup of $S_{2^n}$ contained in the separable permutations. Moreover, the uniform-angle model induces the uniform distribution on this subgroup. For the GOE, GUE, and iid Bernoulli models, the induced permutation is never exactly uniform for $n \\ge 2$. We give the precise rate of departure from uniformity at the leading pivot for the GOE and GUE, and give evidence that this non-uniformity vanishes asymptotically in the permuton sense. In contrast, for banded random matrices of sublinear bandwidth, including the tridiagonal $β$-Hermite ensembles, the induced permutation converges to the diagonal permuton. We further show that the resulting pivot probabilities are sensitive to implementation choices: standard LAPACK routines compare complex pivot candidates using the $\\ell^1$ rather than $\\ell^2$ norm, changing the GUE(2) pivot probability from $1/\\sqrt3$ to $2/3$. Together these results establish a new connection between random matrix theory and permutation combinatorics through numerical linear algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10481",
  "author_total": 3,
  "authors": [
    {
      "name": "Kenji Gunawan"
    },
    {
      "name": "John Peca-Medlin"
    },
    {
      "name": "Chenyang Zhong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c8d50mjs7na5g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10481",
  "fulltext_url": null,
  "id": "c8d50mjs7na5g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10481",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7221058073",
  "pdf_url": "https://arxiv.org/pdf/2610.10481",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c8d50mjs7na5g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10481",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10481"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Random permutations using GEPP",
  "title_text": "Random permutations using GEPP",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/c8d50mjs7na5g",
  "venue": "arXiv",
  "versions": []
}