{
  "abstract": "The first author and Dong \\cite{DD} proposed three conjectures on antichain generating polynomials. Jiang \\cite{Jiang} recently proved Conjectures 4.3 and 4.5, concerning real-rootedness and \\(γ\\)-positivity. We prove Conjecture 4.2 by adapting his method from \\([k]\\times [2] \\times [n]\\) to \\([k]\\times P_{n,s} \\), where \\(P_{n,s}\\) is a two-row Ferrers shape. We establish real stability for a family of bivariate polynomials associated with adjacent shapes, then apply the Chudnovsky-Seymour compatibility criterion to obtain a common interleaver. As noted in \\cite{DD}, Conjecture 4.2 also implies Conjecture 4.3.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25717",
  "author_total": 2,
  "authors": [
    {
      "name": "Jian Ding"
    },
    {
      "name": "Lingen Ding"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6t50vt8vv5q3n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25717",
  "fulltext_url": null,
  "id": "6t50vt8vv5q3n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25717",
  "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",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.25717",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6t50vt8vv5q3n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25717",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25717"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A common interleaver for two antichain polynomials on $[k]$$\\times$ $P_{n,s}$",
  "title_text": "A common interleaver for two antichain polynomials on [k]× P_n,s",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/6t50vt8vv5q3n",
  "venue": "arXiv",
  "versions": []
}