{
  "abstract": "Given a polygon in the plane with vertices on lattice points, Pick's theorem expresses its area A in terms of the number I of lattice points in its interior and the number B of lattice points in its boundary: A = I + B/2 - 1. We consider polygons in the plane whose edges are halfway between lattice points. For such a polygon that is also unimodular, we express its area A in terms of the number I of lattice points in its interior and the number V of its vertices: A = I - V/8 + 1/2 .",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00696",
  "author_total": 2,
  "authors": [
    {
      "name": "Charlene Chu"
    },
    {
      "name": "Yael Karshon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3gdkr9he6m4n3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00696",
  "fulltext_url": null,
  "id": "3gdkr9he6m4n3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00696",
  "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"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7215835648",
  "pdf_url": "https://arxiv.org/pdf/2610.00696",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3gdkr9he6m4n3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00696",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00696"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Pick-type theorem for halfway-lattice polygons",
  "title_text": "A Pick-type theorem for halfway-lattice polygons",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/3gdkr9he6m4n3",
  "venue": "arXiv",
  "versions": []
}