Pith Number

pith:6LZLU2XM

pith:2026:6LZLU2XMHTME4T5CG6BSP5NCBX

not attested not anchored not stored refs resolved

An Erd\H{o}s-Ko-Rado theorem for binary codes

Chi Hoi Yip, Shamil Asgarli

Every maximum 3-wise intersecting family of binary words is a star.

arxiv:2604.13475 v1 · 2026-04-15 · math.CO

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\pithnumber{6LZLU2XMHTME4T5CG6BSP5NCBX}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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 prove that every maximum 3-wise intersecting family is a star. We also present a new proof of the known result for alphabets of size at least 3: maximum intersecting families of words are exactly the stars.

C2weakest assumption

The results hold for sufficiently large word length n (implicit in EKR-type statements); the paper does not specify the exact threshold in the abstract, so the precise range of n for which the statements are claimed is not visible from the provided text.

C3one line summary

For binary words, every maximum 3-wise intersecting family is a star; for alphabets of size at least 3, maximum intersecting families of words are exactly the stars.

References

9 extracted · 9 resolved · 0 Pith anchors

[1] K. Engel and P. Frankl. An Erd ¨os-Ko-Rado theorem for integer sequences of given rank.European J. Combin., 7(3):215–220, 1986 1986

[2] P. Erd ˝os, C. Ko, and R. Rado. Intersection theorems for systems of finite sets.Quart. J. Math. Oxford Ser. (2), 12:313–320, 1961 1961

[3] P. Frankl and Z. F ¨uredi. The Erd¨os-Ko-Rado theorem for integer sequences.SIAM J. Algebraic Discrete Methods, 1(4):376–381, 1980 1980

[4] P. Frankl and N. Tokushige. The Erd ˝os–Ko–Rado theorem for integer sequences.Combinatorica, 19(1):55–63, 1999 1999

[5] C. Godsil and K. Meagher.Erd ˝os-Ko-Rado theorems: algebraic approaches, volume 149 ofCambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2016 2016

Receipt and verification

First computed	2026-06-19T16:10:37.402511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2f2ba6aec3cd84e4fa2378327f5a20dcc3bceadb0adb12570eef9b868e0015d

Aliases

arxiv: 2604.13475 · arxiv_version: 2604.13475v1 · doi: 10.48550/arxiv.2604.13475 · pith_short_12: 6LZLU2XMHTME · pith_short_16: 6LZLU2XMHTME4T5C · pith_short_8: 6LZLU2XM

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/6LZLU2XMHTME4T5CG6BSP5NCBX \
  | 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: f2f2ba6aec3cd84e4fa2378327f5a20dcc3bceadb0adb12570eef9b868e0015d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02e0a94618cd11de0235affdd3990979e76e0f458a0bbed4b2c9529b355aeeac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-04-15T04:57:17Z",
    "title_canon_sha256": "d5cd8e11caaf515e888ab0778fb8f7a9458830384b3ea223752d73ddaf79ea5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.13475",
    "kind": "arxiv",
    "version": 1
  }
}