{
  "abstract": "The Ehrhart polynomial and Ehrhart series count lattice points in integer dilations of a lattice polytope. We introduce and study a q -deformation of the Ehrhart series, based on the notions of harmonic spaces and Macaulay’s inverse systems for coordinate rings of finite point configurations. We conjecture that this q -Ehrhart series is a rational function, and introduce and study a bigraded algebra whose Hilbert series matches the q -Ehrhart series. Defining this algebra requires a new result on Macaulay inverse systems for Minkowski sums of point configurations.",
  "abstract_shown": true,
  "affiliations": [
    "University of Minnesota, Minneapolis, USA",
    "University of California, San Diego, USA"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Victor Reiner",
      "orcid": "0000-0002-1816-5693"
    },
    {
      "affs": [
        1
      ],
      "name": "Brendon Rhoades",
      "orcid": "0000-0003-0433-5185"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/95g2dw7pkftkb.bib",
  "cited_by": 15,
  "doi": "10.4171/jca/128",
  "fulltext_url": null,
  "id": "95g2dw7pkftkb",
  "issns": [
    "2415-6302",
    "2415-6310"
  ],
  "landing_url": "https://doi.org/10.4171/jca/128",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W4400518785",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-19",
  "publisher": "EMS Press",
  "ris": "https://research.draconitic.com/paper/95g2dw7pkftkb.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T13:20:36Z",
      "native_id": "W4400518785",
      "source": "openalex",
      "url": "https://doi.org/10.4171/jca/128"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2602|Commutative Algebra and Its Applications",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Harmonics and graded Ehrhart theory",
  "title_text": "Harmonics and graded Ehrhart theory",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T13:20:36Z",
  "url": "https://research.draconitic.com/paper/95g2dw7pkftkb",
  "venue": "Journal of Combinatorial Algebra",
  "versions": []
}