{
  "abstract": "Beck and Pixton expressed the Ehrhart polynomial of the Birkhoff polytope as a weighted sum of constant terms of several multivariate rational functions. Xin and Zhang studied a class of constant terms $h_n(t)$, which can be regarded as a variation of the Morris constant term. They proved that $h_n(t)$ is a polynomial of degree $(n-1)^2$ and obtained many nice properties involving the Morris constant term identity. Let $h_n^*(y)=(1-y)^{(n-1)^2+1}\\sum_{t\\geq0}h_n(t)y^t$. For fixed $n\\geq 3$, we obtain the following results for $h_n^*(y)$: (i): $h_n^*(y)$ is a polynomial with positive integer coefficients. (ii): $h_n^*(y)$ is real-rooted. In particular, all its roots are non-positive real numbers. (iii): $h_n^*(y)$ is Gamma-positive. Furthermore, $h_n^*(y)$ is palindromic, unimodal, and ultra log-concave. This confirms Xin and Zhang's conjecture regarding $h_n^*(y)$. In order to resolve this conjecture, we also developed an operator on the space of symmetric polynomials that preserves real stability. As a byproduct, we prove that every root of a Gamma polynomial associated with $h_n^*(y)$ is a negative real number.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15201",
  "author_total": 2,
  "authors": [
    {
      "name": "Feihu Liu"
    },
    {
      "name": "Zihao Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0j2ew9e4pkf5s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15201",
  "fulltext_url": null,
  "id": "0j2ew9e4pkf5s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15201",
  "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",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213292361",
  "pdf_url": "https://arxiv.org/pdf/2609.15201",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0j2ew9e4pkf5s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2609.15201",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15201"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Real-Rootedness and Gamma-Positivity for a Variation of the Morris Constant Term",
  "title_text": "Real-Rootedness and Gamma-Positivity for a Variation of the Morris Constant Term",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/0j2ew9e4pkf5s",
  "venue": "arXiv",
  "versions": []
}