Pith Number

pith:S2YIMHIC

pith:2026:S2YIMHICNC2EOUCID2DQ6FXNPZ

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Uniform Tur\'an densities of $k$-uniform hypergraphs

Guanghui Wang, Guowei Sun, Hao Lin, Wenling Zhou

For any family of k-graphs, the (k-2)-uniform Turán density equals the palette Turán density.

arxiv:2605.15105 v1 · 2026-05-14 · math.CO

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Claims

C1strongest claim

For every family F of k-graphs, we prove that π_{k-2}(F) equals the corresponding palette Turán density. ... we establish the following values [list of six expressions] as (k-2)-uniform Turán densities of single k-graphs. Finally ... there exist k-graphs F1,F2 such that π_{k-2}({F1,F2}) < min{π_{k-2}(F1),π_{k-2}(F2)}.

C2weakest assumption

The palette classification tools correctly characterize the existence of k-graphs satisfying prescribed palette colorability constraints, and these tools apply without hidden restrictions on the underlying vertex sets or color palettes.

C3one line summary

A new palette framework reduces (k-2)-uniform Turán densities of k-graphs to palette-homomorphism problems and yields exact values including (r-1)/r, (r-1)^2/r^2, and (k-1)^k/k^k for various k and r.

References

31 extracted · 31 resolved · 0 Pith anchors

[1] J. Balogh. The Turán density of triple systems is not principal.J. Combin. Theory Ser. A, 100(1):176–180, 2002 2002

[2] Colloq., Balatonfüred, 1969), volume 4 ofColloq 1969

[3] M. Bucić, J. W. Cooper, D. Král’, S. Mohr, and D. Munhá Correia. Uniform Turán density of cycles.Trans. Amer. Math. Soc., 376(7):4765–4809, 2023 2023

[4] A. Y. Chen and B. Schülke. Beyond the broken tetrahedron.Combin. Probab. Comput., 35(1):59–70, 2026 2026

[5] O. Cooley, N. Fountoulakis, D. Kühn, and D. Osthus. Embeddings and Ramsey numbers of sparsek-uniform hypergraphs.Combinatorica, 29(3):263–297, 2009 2009

Formal links

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Receipt and verification

First computed	2026-05-17T21:40:25.795609Z
Last reissued	2026-05-17T21:57:19.127486Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

96b0861d0268b44750481e870f16ed7e66f67f2541bc6a94034cac7b8d8f706d

Aliases

arxiv: 2605.15105 · arxiv_version: 2605.15105v1 · pith_short_12: S2YIMHICNC2E · pith_short_16: S2YIMHICNC2EOUCI · pith_short_8: S2YIMHIC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/S2YIMHICNC2EOUCID2DQ6FXNPZ \
  | 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: 96b0861d0268b44750481e870f16ed7e66f67f2541bc6a94034cac7b8d8f706d

Canonical record JSON

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    "abstract_canon_sha256": "e7ef263ca68272e1c715e7b6c3328fa0be845b7c39f3369a9f82221595dccc0c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-14T17:23:04Z",
    "title_canon_sha256": "d7efcb6681589ed4655b3c175f2aec4379df8cb87e7827bb456f500ead80b6a9"
  },
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  "source": {
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    "kind": "arxiv",
    "version": 1
  }
}