{
  "id": "1406.0142",
  "version": "v2",
  "published": "2014-06-01T08:22:45.000Z",
  "updated": "2022-03-14T17:41:03.000Z",
  "title": "Orthogonal basis for functions over a slice of the Boolean hypercube",
  "authors": [
    "Yuval Filmus"
  ],
  "comment": "21 pages",
  "journal": "Electronic Journal of Combinatorics, volume 23, issue 1, article number P1.23, 2016",
  "doi": "10.37236/4567",
  "categories": [
    "math.CO"
  ],
  "abstract": "We present an orthogonal basis for functions over a slice of the Boolean hypercube. Our basis is also an orthogonal basis of eigenvectors for the Johnson and Kneser graphs. As an application of our basis, we streamline Wimmer's proof of Friedgut's theorem for slices of the Boolean hypercube.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-01T08:22:45.000Z",
      "comment": "18 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2022-03-14T17:41:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E30"
    ],
    "keywords": [
      "boolean hypercube",
      "orthogonal basis",
      "streamline wimmers proof",
      "kneser graphs",
      "friedguts theorem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}