{
  "annotation_id": "e7d897e5-1e8d-41ce-915e-43eba0c83434",
  "date_created": "2026-03-02T18:02:34.257000Z",
  "date_modified": "2026-03-02T18:02:34.257000Z",
  "file_hash": "6e334b653c522cc6f1cd6d96b09f6adf29b6b94bf3a1dd1d1ff532107176f7f8",
  "private": false,
  "record": {
    "abstract": "Krawtchouk matrices have as entries values of the Krawtchouk polynomials for\nnonnegative integer arguments. We show how they arise as condensed\nSylvester-Hadamard matrices via a binary shuffling function. The underlying\nsymmetric tensor algebra is presented. Our approach is used to solve Kac\u0027\nformulation of the Ehrenfest urn model. Connections with quantum and classical\nrandom walks are shown as well as various extensions of the classical\npolynomials.",
    "arxiv_id": "quant-ph/0702073",
    "authors": [
      "Philip Feinsilver",
      "Jerzy Kocik"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Recent advances in applied probability, Springer-Verlag, October,\n  2004",
    "title": "Krawtchouk polynomials and Krawtchouk matrices",
    "url": "https://arxiv.org/abs/quant-ph/0702073"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "161f5c91-61ed-4609-bee6-a99ca04a85a2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}