{
  "id": "1110.5540",
  "version": "v1",
  "published": "2011-10-25T15:40:37.000Z",
  "updated": "2011-10-25T15:40:37.000Z",
  "title": "Cubic Harmonics and Bernoulli Numbers",
  "authors": [
    "Katsunori Iwasaki"
  ],
  "comment": "18 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The functions satisfying the mean value property for an n-dimensional cube are determined explicitly. This problem is related to invariant theory for a finite reflection group, especially to a system of invariant differential equations. Solving this problem is reduced to showing that a certain set of invariant polynomials forms an invariant basis. After establishing a certain summation formula over Young diagrams, the latter problem is settled by considering a recursion formula involving Bernoulli numbers. Keywords: polyhedral harmonics; cube; reflection groups; invariant theory; invariant differential equations; generating functions; partitions; Young diagrams; Bernoulli numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-25T15:40:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B15",
      "20F55",
      "11B68"
    ],
    "keywords": [
      "bernoulli numbers",
      "cubic harmonics",
      "invariant differential equations",
      "young diagrams",
      "invariant theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.5540I"
    }
  }
}