{
  "abstract": "In Ehrhart theory, the local h * -polynomial is a fundamental invariant of a lattice polytope. Its coefficient vector, the local h * -vector, is the coefficient vector of the top degree part of the Hodge-Deligne polynomial of the primitive cohomology with compact support of the associated generic hypersurface in the algebraic torus. In the literature on hypergeometric motives, the Hodge vector of a lattice polytope is its local h * -vector with leading and trailing zeroes removed. Of recent special interest are thin polytopes whose Hodge vectors vanish.\n\nGiven lattice polytopes P 1 , ⋯ , P k contained in a k -dimensional subspace U ⊆ ℝ d and a d -dimensional lattice polytope P ⊂ ℝ d , we compute the Hodge vector of the Cayley polytope P 1 * ⋯ * P k * P , and show that it equals the mixed volume of P 1 , ... , P k times the Hodge vector of the projection of P along U . This allows finding infinitely many high-dimensional lattice polytopes with the same Hodge vector that are not free joins. The proof relies on a closed formula for the Hodge-Deligne polynomial of generic complete intersections in the torus in terms of the bivariate/mixed h * -polynomial. A special case of our construction is what we call Lawrence twists: extending the Gale transform by centrally-symmetric pairs of vectors. As applications, we can produce many new thin polytopes answering a question by Borger, Kretschmer and the second author, and we provide an alternative explanation of the thinness of B k -polytopes answering a question of Selyanin.",
  "abstract_shown": true,
  "affiliations": [
    "Otto-von-Guericke-Universität Magdeburg, Faculty of Mathematics, Universitätsplatz 2, 39106 Magdeburg (Germany)"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Vadym Kurylenko"
    },
    {
      "affs": [
        0
      ],
      "name": "Benjamin Nill"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cfrx4rtdxb8xa.bib",
  "cited_by": 0,
  "doi": "10.5802/alco.515",
  "fulltext_url": null,
  "id": "cfrx4rtdxb8xa",
  "issns": [
    "2589-5486"
  ],
  "landing_url": "https://alco.centre-mersenne.org/articles/10.5802/alco.515/",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7131431770",
  "pdf_url": "https://alco.centre-mersenne.org/item/10.5802/alco.515.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": "MathDoc/Centre Mersenne",
  "ris": "https://research.draconitic.com/paper/cfrx4rtdxb8xa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:25Z",
      "native_id": "10.5802/alco.515",
      "source": "crossref",
      "url": "https://alco.centre-mersenne.org/articles/10.5802/alco.515/"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Advanced Combinatorial Mathematics",
      "subfield": "combinatorics"
    }
  ],
  "title": "Preserving Hodge vectors of lattice polytopes",
  "title_text": "Preserving Hodge vectors of lattice polytopes",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:25Z",
  "url": "https://research.draconitic.com/paper/cfrx4rtdxb8xa",
  "venue": "Algebraic Combinatorics",
  "versions": []
}