{
  "id": "2410.19138",
  "version": "v1",
  "published": "2024-10-24T20:13:47.000Z",
  "updated": "2024-10-24T20:13:47.000Z",
  "title": "Spectrality of the product does not imply that the components are spectral",
  "authors": [
    "Gábor Somlai"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Greenfeld and Lev conjectured that the Cartesian product of two sets $A$ and $B$ is spectral if and only if $A$ and $B$ are spectral. We construct a counterexample to this fact using the existence of a tile that has no spectra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-24T20:13:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectrality",
      "components",
      "cartesian product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}