{
  "id": "2505.06941",
  "version": "v1",
  "published": "2025-05-11T11:13:50.000Z",
  "updated": "2025-05-11T11:13:50.000Z",
  "title": "When are Hopf algebras determined by integer sequences?",
  "authors": [
    "Nicolas Andrews",
    "Lucas Gagnon",
    "Félix Gélinas",
    "Eric Schlums",
    "Mike Zabrocki"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We study the category of graded Hopf algebras that are free noncommutative, cocommutative, graded and connected from the perspective of the sequences of dimensions of the graded pieces. We show that a Hopf algebra exists with a given sequence of graded dimensions if and only if the ``INVERTi'' transformation of the sequence is nonnegative. We give conditions on the sequences of graded dimensions for two Hopf algebras $H$ and $K$ in this category under which there exists a surjective homomorphism from $H$ to $K$. We also give conditions such that an isomorphic copy of $H$ occurs as a Hopf subalgebra of $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-11T11:13:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16T30"
    ],
    "keywords": [
      "integer sequences",
      "graded dimensions",
      "graded hopf algebras",
      "conditions",
      "isomorphic copy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}