{
  "annotation_id": "94b65f28-5323-4d4e-b13c-3f7d4d2b93f2",
  "date_created": "2026-02-17T05:53:15.712000Z",
  "date_modified": "2026-02-17T05:53:15.712000Z",
  "file_hash": "5a66509303756080e1bd60e67edf8b2245df73378807ace2cef4e40eac7933b2",
  "private": false,
  "record": {
    "abstract": "Let us denote elements of the symmetric group $S_n$ using square brackets for the one-line notation. Cycles will be represented using parentheses, following the standard cycle notation. Under this convention, the full reversal of the identity element $()$ is the element $s = [n\\ n-1 \\dots 1]$. In the present work, we obtain a lower bound on the decomposition complexity of elements $s(1n \\dots 2)^{i}$ into the generators $(12), (12 \\dots n), (1n \\dots 2)$, where $i$ ranges over the set $\\{1,2,\\dots,n\\}$. As a consequence, we derive the lower bound $n(n-1)/2$ for the diameter of Cayley graph of the group $S_n$ generated by $(12), (12 \\dots n), (1n \\dots 2)$.",
    "arxiv_id": "2601.08715",
    "authors": [
      "Grigorii Antiufeev"
    ],
    "categories": [
      "math.CO",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "A Lower Bound for the Diameter of Cayley Graph of the Symmetric Group $S_n$ Generated by $(12), (12 \\dots n), (1n \\dots 2)$",
    "url": "https://arxiv.org/abs/2601.08715",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d74fbd98-a376-4400-b014-81ece93ed510",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}