Pith Number

pith:Q4DGKEQS

pith:2026:Q4DGKEQSAM7J2ZVGWSVDEAH5LC

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A Lower Bound for the Diameter of Cayley Graph of the Symmetric Group $S_n$ Generated by $(12), (12 \dots n), (1n \dots 2)$

Grigorii Antiufeev

The diameter of the Cayley graph of S_n generated by (12), (12…n), (1n…2) is at least n(n-1)/2.

arxiv:2601.08715 v3 · 2026-01-13 · math.CO · math.GR

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\usepackage{pith}
\pithnumber{Q4DGKEQSAM7J2ZVGWSVDEAH5LC}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

we derive the lower bound n(n-1)/2 for the diameter of Cayley graph of the group S_n generated by (12), (12 … n), (1n … 2)

C2weakest assumption

That a lower bound on the word length of the specific family s(1n…2)^i for i=1 to n is sufficient to lower-bound the diameter of the entire Cayley graph (i.e., that the diameter is realized or exceeded by one of these elements).

C3one line summary

A lower bound of n(n-1)/2 is established for the diameter of the Cayley graph of S_n generated by (12), (12...n), and (1n...2).

Receipt and verification

First computed	2026-06-05T01:14:33.089162Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8706651212033e9d66a6b4aa3200fd5898bc564a7a97d0c2f4b5e95fea2d884a

Aliases

arxiv: 2601.08715 · arxiv_version: 2601.08715v3 · doi: 10.48550/arxiv.2601.08715 · pith_short_12: Q4DGKEQSAM7J · pith_short_16: Q4DGKEQSAM7J2ZVG · pith_short_8: Q4DGKEQS

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Q4DGKEQSAM7J2ZVGWSVDEAH5LC \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8706651212033e9d66a6b4aa3200fd5898bc564a7a97d0c2f4b5e95fea2d884a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12d32e71e35ec2556fcbc92742d655dd9e314e1699260918bb6067154fedb979",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-01-13T16:41:58Z",
    "title_canon_sha256": "effe7737032aae7b2e28ba2b07894fcccd20453e0667b710550af6b5981db833"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.08715",
    "kind": "arxiv",
    "version": 3
  }
}