Pith Number

pith:ADOS4MWU

pith:2026:ADOS4MWUQS6K6CCOGFKU6USNHU

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On the independence number of de Bruijn graphs

Matteo Novaga, Pietro Majer

The independence number of the de Bruijn graph B(k,q) equals λ_{k-1} q^k plus a smaller term, where λ_{k-1} is the value of a variational problem on the unit (k-1)-cube.

arxiv:2604.14671 v2 · 2026-04-16 · math.CO · cs.IT · math.IT

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Claims

C1strongest claim

We derive the asymptotic formula α(k,q)=λ_{k-1}q^k+o(q^k), where λ_{k-1} is a constant arising from a variational problem on the unit (k-1)-dimensional cube. ... For k=11 and k=13 this yields certified optimal constructions, which combined with a lifting theorem by Lichiardopol give exact formulas for α(11,q) and α(13,q) for all q≥2.

C2weakest assumption

The variational problem on the (k-1)-cube correctly captures the asymptotic density of maximum independent sets, and the phase-reduction constructions for odd-prime k are optimal in the binary case so that the cited lifting theorem extends them exactly to all q.

C3one line summary

α(k,q) = λ_{k-1} q^k + o(q^k) where λ_{k-1} arises from a variational problem on the (k-1)-cube; exact formulas hold for k=11,13 via phase reduction and lifting, with bounds 91/240 ≤ λ_3 ≤ 11/28 for k=4.

Receipt and verification

First computed	2026-06-11T01:09:35.654748Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00dd2e32d484bcaf084e31554f524d3d135c964c6611190fa56688fc5205b931

Aliases

arxiv: 2604.14671 · arxiv_version: 2604.14671v2 · doi: 10.48550/arxiv.2604.14671 · pith_short_12: ADOS4MWUQS6K · pith_short_16: ADOS4MWUQS6K6CCO · pith_short_8: ADOS4MWU

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ADOS4MWUQS6K6CCOGFKU6USNHU \
  | 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: 00dd2e32d484bcaf084e31554f524d3d135c964c6611190fa56688fc5205b931

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0386ae242a656c2168dd42cf7499b1b56d4cb4ae3c3213777720c59253ced8a7",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-04-16T06:28:49Z",
    "title_canon_sha256": "7bf300320d4201f32ecce59977c4c06d09785493e6c5e8a4d09000a98de52d26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.14671",
    "kind": "arxiv",
    "version": 2
  }
}