Pith Number

pith:76TVUVQ6

pith:2025:76TVUVQ6B2XVWTW7G7MAAE4I7M

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Yamaguti algebras and noncrossing partitions

Fr\'ed\'eric Chapoton (IRMA), Vladimir Dotsenko (IRMA)

The nonsymmetric operad of Yamaguti algebras is described combinatorially by noncrossing partitions without singleton blocks.

arxiv:2510.03148 v2 · 2025-10-03 · math.AT · math.CO

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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 show that the nonsymmetric operad of Yamaguti algebras admit a simple combinatorial description via noncrossing partitions without singleton blocks.

C2weakest assumption

The paper takes the definition of Yamaguti algebras introduced by Das as the correct starting point and assumes that the nonsymmetric operad structure is faithfully captured by the chosen combinatorial objects without missing relations or extraneous elements.

C3one line summary

Nonsymmetric operad of Yamaguti algebras admits combinatorial description via noncrossing partitions without singleton blocks.

References

20 extracted · 20 resolved · 0 Pith anchors

[1] The local h-vector of the cluster subdivision of a simplex 2011

[2] Irreducible Lie- Yamaguti algebras 2009

[3] Irreducible Lie- Yamaguti algebras of generic type 2011

[4] A polynomial identity for the bilinear operation in Lie-Yamaguti algebras 2014

[5] Bremner and Vladimir Dotsenko 2016

Receipt and verification

First computed	2026-06-23T01:11:57.539435Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffa75a561e0eaf5b4edf37d8001388fb012bdcf2e4612da2874bd4f294639650

Aliases

arxiv: 2510.03148 · arxiv_version: 2510.03148v2 · doi: 10.48550/arxiv.2510.03148 · pith_short_12: 76TVUVQ6B2XV · pith_short_16: 76TVUVQ6B2XVWTW7 · pith_short_8: 76TVUVQ6

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/76TVUVQ6B2XVWTW7G7MAAE4I7M \
  | 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: ffa75a561e0eaf5b4edf37d8001388fb012bdcf2e4612da2874bd4f294639650

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e1de6bcec018e69ef8f9b070bff2e727710f583ef874e04f646d9d03c50d4d3",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2025-10-03T16:20:47Z",
    "title_canon_sha256": "82aa29b4ce9316c98c19e6f42464babec41379650849380f482191f3dcdbc5e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.03148",
    "kind": "arxiv",
    "version": 2
  }
}