{
  "id": "cond-mat/0104293",
  "version": "v1",
  "published": "2001-04-17T10:22:11.000Z",
  "updated": "2001-04-17T10:22:11.000Z",
  "title": "Partition functions and symmetric polynomials",
  "authors": [
    "H. -J. Schmidt",
    "J. Schnack"
  ],
  "comment": "10 pages, no figures; submitted to Am. J. Phys.. More information at http://www.physik.uni-osnabrueck.de/makrosysteme/",
  "journal": "Am. J. Phys. 70 (2002) 53-57",
  "doi": "10.1119/1.1412643",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We find a close correspondence between certain partition functions of ideal quantum gases and certain symmetric polynomials. Due to this correspondence it can be shown that a number of thermodynamic identities which have recently been considered are essentially of combinatorical origin and known for a long time as theorems on symmetric polynomials. For example, a recurrence relation for partition functions appearing in the textbook of P. Landsberg is nothing else but Newton's identity in disguised form. Conversely, a certain theorem on symmetric polynomials translates into a new and unexpected relation between fermionic and bosonic partition functions, which can be used to express the former by means of the latter and vice versa.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-04-17T10:22:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ideal quantum gases",
      "symmetric polynomials translates",
      "bosonic partition functions",
      "thermodynamic identities",
      "close correspondence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}