{
  "abstract": "We prove real-rootedness for the Chow polynomials of the noncrossing partition lattices by transferring tieless parking functions to finite-alphabet Smirnov words and applying an interlacing-preserving transition of M.~Leander. We also derive a triangular recurrence for peaks and ties and identify the peakless-tieless descent polynomial as the Narayana polynomial. For the toric $g$-contributions of Ehrenborg--Hetyei--Readdy, we exhibit a fixed-row common interlacer and establish real-rootedness of all nonnegative row sums. Individual real-rootedness follows in particular; Q.~Xiao also proved it by a different differential recurrence. We also give a second proof of the individual statement, by finite Schur--Szegő convolution, that does not use the common interlacer. These results prove Conjecture~4.2 of Xiao and Conjecture~11.2 of Ehrenborg--Hetyei--Readdy, with consequences for weakly 123-avoiding parking functions. We also prove real-rootedness for the image-size polynomial on all parking functions and for the ascent and descent polynomials of four two-pattern-avoiding classes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05131",
  "author_total": 1,
  "authors": [
    {
      "name": "Per Alexandersson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4v7yg0jft85c7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05131",
  "fulltext_url": null,
  "id": "4v7yg0jft85c7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05131",
  "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"
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    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
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  ],
  "openalex": "W7211904147",
  "pdf_url": "https://arxiv.org/pdf/2609.05131",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4v7yg0jft85c7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.05131",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05131"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Real-rootedness and interlacing for parking functions and Chow polynomials",
  "title_text": "Real-rootedness and interlacing for parking functions and Chow polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/4v7yg0jft85c7",
  "venue": "arXiv",
  "versions": []
}