{
  "id": "2111.01018",
  "version": "v3",
  "published": "2021-11-01T15:23:29.000Z",
  "updated": "2022-10-22T05:30:51.000Z",
  "title": "Extremal sequences for a weighted zero-sum constant",
  "authors": [
    "Santanu Mondal",
    "Krishnendu Paul",
    "Shameek Paul"
  ],
  "comment": "18 pages. arXiv admin note: substantial text overlap with arXiv:2110.02539",
  "categories": [
    "math.NT"
  ],
  "abstract": "The constant $C_A(n)$ is defined to be the smallest natural number $k$ such that any sequence of $k$ elements in $\\mathbb Z_n$ has a subsequence of consecutive terms whose $A$-weighted sum is zero, where the weight set $A\\subseteq \\mathbb Z_n\\setminus \\{0\\}$. If $C_A(n)=k$, then a sequence in $\\mathbb Z_n$ of length $k-1$ which has no $A$-weighted zero-sum subsequence of consecutive terms is called an $A$-extremal sequence. We characterize these sequences for some particular weight sets.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-10-22T05:30:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B50"
    ],
    "keywords": [
      "weighted zero-sum constant",
      "extremal sequence",
      "weight set",
      "smallest natural number",
      "consecutive terms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}