{
  "id": "1505.05745",
  "version": "v1",
  "published": "2015-05-21T14:06:11.000Z",
  "updated": "2015-05-21T14:06:11.000Z",
  "title": "A family of measures on symmetric groups and the field with one element",
  "authors": [
    "Jeffrey C. Lagarias"
  ],
  "comment": "24 pages, comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "For each positive integer n this paper considers a one-parameter family of complex-valued measures on the symmetric group S_n, depending on a complex parameter z. For parameter values z=p^k a prime power, this measure describes splitting probabilities for monic degree n polynomials over the finite field with p^k elements, conditioned on being square-free. It studies these measure in the special case z=1, and shows they have an interesting internal structure having a representation theoretic interpretation. These measures may provide data relevant to the hypothetical \"field with one element.\"",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-21T14:06:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric group",
      "representation theoretic interpretation",
      "data relevant",
      "interesting internal structure",
      "complex parameter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150505745L"
    }
  }
}