{
  "id": "2008.03279",
  "version": "v1",
  "published": "2020-08-04T07:34:26.000Z",
  "updated": "2020-08-04T07:34:26.000Z",
  "title": "About finite posets R and S with \\# H(P,R) <= \\# H(P,S) for every finite poset P",
  "authors": [
    "Frank a Campo"
  ],
  "comment": "24 pages, 7 figures. arXiv admin note: text overlap with arXiv:arXiv:1908.06897",
  "categories": [
    "math.CO"
  ],
  "abstract": "Finite posets $R$ and $S$ are studied with $\\# {\\cal H}(P,R) \\leq \\# {\\cal H}(P,S)$ for every finite poset $P$, where ${\\cal H}(P,Q)$ is the set of order homomorphisms from $P$ to $Q$. It is shown that under an additional regularity condition, $\\# {\\cal H}(P,R) \\leq \\# {\\cal H}(P,S)$ for every finite poset $P$ is equivalent to $\\# {\\cal S}(P,R) \\leq \\# {\\cal S}(P,S)$ for every finite poset $P$, where ${\\cal S}(P,Q)$ is the set of strict order homomorphisms from $P$ to $Q$. A method is developed for the rearrangement of a finite poset $R$, resulting in a poset $S$ with $\\# {\\cal H}(P,R) \\leq \\# {\\cal H}(P,S)$ for every finite poset $P$. The results are used in constructing pairs of posets $R$ and $S$ with this property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-04T07:34:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06A07",
      "06A06"
    ],
    "keywords": [
      "finite poset",
      "strict order homomorphisms",
      "additional regularity condition",
      "equivalent",
      "rearrangement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}