{
  "abstract": "The alternating composition of $N = 2p$ weighted differential operators $w_j(x)\\cdot\\partial_x^{\\,p}$ of strict order $p$ on the line $\\mathbb{R} \\ni x$ is again an operator of order $p$; its coefficient is the universal constant $c(p)$ times the Wronskian of the weights $w_1,\\ldots,w_N$. Lie brackets of vector fields fix $c(p=1)=1$; we want to find $c(p \\geqslant 2)$: e.g., $c(2) = 2$ or $c(3) = 90$. Direct symbolic expansion (over $|S_{2p}| =(2p)!$ permutations) fails for $p \\geqslant 4$. Taking the monomials $w_j = x^{j-1}$ reduces the summation to the much smaller set $Φ_p \\subseteq S_{2p-1} \\subsetneq S_{2p}$ of late-growing permutations. Expressing $c(p)$ as a signed sum of products of falling factorials, we implement and speed up the algorithm that gains all the integer values up to $c(18) = 4.881\\ldots \\cdot 10^{462}$. The resulting sequence is new, now registered as OEIS A392714; its (sub)leading-order growth rate is $\\log c(p) \\simeq 2p^2\\log p -b p^2 + \\overline{o}(p^2)$ for $p\\gg 1$, with $b\\geqslant 2.6744$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08636",
  "author_total": 2,
  "authors": [
    {
      "name": "Kian C. Shah"
    },
    {
      "name": "Arthemy V. Kiselev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1feeezt79xtx1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08636",
  "fulltext_url": null,
  "id": "1feeezt79xtx1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08636",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7221040424",
  "pdf_url": "https://arxiv.org/pdf/2610.08636",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1feeezt79xtx1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08636",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08636"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "New integer sequence OEIS A392714 counts Wronskians: fast evaluation via late-growing permutations",
  "title_text": "New integer sequence OEIS A392714 counts Wronskians: fast evaluation via late-growing permutations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/1feeezt79xtx1",
  "venue": "arXiv",
  "versions": []
}