{
  "abstract": "We prove multivariate stability for a class of affine triangular recurrences whose two coefficients are raised to an arbitrary positive integer power. The variables keep track of cross-step heights in a weighted lattice-path model. The applications include stability and real rootedness of parametrised Eulerian, Stirling, and Lah families. For the parametrised Eulerian polynomials, we obtain multivariate refinements of known real-rootedness results and prove simplicity and strict interlacing of consecutive rows. A kernel-preserving bijection with increasing binary trees yields a synchronised Foata--Strehl action on pairs and a combinatorial interpretation of their gamma coefficients along with a recurrence. The same bijection identifies refinement posets that admit symmetric Boolean and chain decompositions for parameter one and cover-supported $\\mathfrak{sl}_2$ operators prove their PECKness. We extend the stability and strict interlacing results to synchronised Stirling permutations and prove PECKness for ordinary Stirling permutations with a fixed number of plateaux.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15651",
  "author_total": 1,
  "authors": [
    {
      "name": "Umesh Shankar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fzcc2b446x1xp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15651",
  "fulltext_url": null,
  "id": "fzcc2b446x1xp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15651",
  "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"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213229097",
  "pdf_url": "https://arxiv.org/pdf/2609.15651",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fzcc2b446x1xp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15651",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15651"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Multivariate stability of powered triangular recurrences and parametrised Eulerian polynomials",
  "title_text": "Multivariate stability of powered triangular recurrences and parametrised Eulerian polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/fzcc2b446x1xp",
  "venue": "arXiv",
  "versions": []
}