{
  "abstract": "In this paper, we consider the magic positivity of the Ehrhart polynomial of dilated base polytope of minimal matroid of rank $k$ dimension $n$. We prove that for $\\displaystyle 1\\leq k<\\lfloor\\frac{n}{2}\\rfloor$, the $n-k-1$ dilate of the Ehrhart polynomial is not magic positive. We also show that for sufficiently large $n$, the $n-k$ dilate of the Ehrhart polynomial is, in general, magic positive. This gives rise to a lower bound of the $m-$index of the Ehrhart polynomial.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32050",
  "author_total": 5,
  "authors": [
    {
      "name": "Jiaxuan Chen"
    },
    {
      "name": "Chance Crigler"
    },
    {
      "name": "Shengtao Ding"
    },
    {
      "name": "Dana Paquin"
    },
    {
      "name": "Julian Schennach"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b2c4kagmcfekq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32050",
  "fulltext_url": null,
  "id": "b2c4kagmcfekq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32050",
  "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"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7223662395",
  "pdf_url": "https://arxiv.org/pdf/2610.32050",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b2c4kagmcfekq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.32050",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32050"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the magic positivity of the Ehrhart polynomials of dilated base polytope of minimal matroid",
  "title_text": "On the magic positivity of the Ehrhart polynomials of dilated base polytope of minimal matroid",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/b2c4kagmcfekq",
  "venue": "arXiv",
  "versions": []
}