{
  "id": "2405.01164",
  "version": "v1",
  "published": "2024-05-02T10:36:37.000Z",
  "updated": "2024-05-02T10:36:37.000Z",
  "title": "Clonoids of Boolean functions with a monotone or discriminator source clone",
  "authors": [
    "Erkko Lehtonen"
  ],
  "comment": "38 pages",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "abstract": "Extending Sparks's theorem, we determine the cardinality of the lattice of $(C_1,C_2)$-clonoids of Boolean functions in the cases where the target clone $C_2$ is the clone of projections. Moreover, we explicitly describe the $(C_1,C_2)$-clonoids of Boolean functions in the cases where the source clone $C_1$ is one of the four clones of monotone functions or contains the discriminator function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-02T10:36:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boolean functions",
      "discriminator source clone",
      "extending sparkss theorem",
      "discriminator function",
      "monotone functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}