{
  "annotation_id": "6ffced64-3ccb-4c95-ba3d-12cf379fab03",
  "date_created": "2026-03-02T18:02:03.404000Z",
  "date_modified": "2026-03-02T18:02:03.404000Z",
  "file_hash": "c5f8087353805e4948121a5a3a89040dac5305ff5b426d3b678ae7b2ae0c75d3",
  "private": false,
  "record": {
    "abstract": "We consider the transformation properties of integer sequences arising from\nthe normal ordering of exponentiated boson ([a,a*]=1) monomials of the form\nexp(x (a*)^r a), r=1,2,..., under the composition of their exponential\ngenerating functions (egf). They turn out to be of Sheffer-type. We demonstrate\nthat two key properties of these sequences remain preserved under\nsubstitutional composition: (a)the property of being the solution of the\nStieltjes moment problem; and (b) the representation of these sequences through\ninfinite series (Dobinski-type relations). We present a number of examples of\nsuch composition satisfying properties (a) and (b). We obtain new Dobinski-type\nformulas and solve the associated moment problem for several hierarchically\ndefined combinatorial families of sequences.",
    "arxiv_id": "quant-ph/0312202",
    "authors": [
      "K. A. Penson",
      "P. Blasiak",
      "G. Duchamp",
      "A. Horzela",
      "A. I. Solomon"
    ],
    "categories": [
      "quant-ph",
      "math.CO"
    ],
    "doi": "10.1088/0305-4470/37/10/011",
    "journal_ref": "J.Phys.A:Math.Gen.37 (2004)3475-3487",
    "title": "Hierarchical Dobinski-type relations via substitution and the moment   problem",
    "url": "https://arxiv.org/abs/quant-ph/0312202"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a0e52584-058f-40d1-ae9e-30112545f589",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}