Pith Number

pith:3LW6L3AB

pith:2026:3LW6L3AB4F4DRNBIO6QUEKQLLE

not attested not anchored not stored refs resolved

Double shortcuts of standard hypercube decompositions

Margherita Zannoni

A conjecture on double shortcuts holds for standard hypercube decompositions of Bruhat intervals in the symmetric group.

arxiv:2605.13304 v1 · 2026-05-13 · math.CO · math.RT

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\usepackage{pith}
\pithnumber{3LW6L3AB4F4DRNBIO6QUEKQLLE}

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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

Our results imply that a conjecture stated in [Bull. London Math. Soc., 57 (2025), no. 8] holds for the class of standard hypercube decompositions.

C2weakest assumption

The results apply specifically to standard hypercube decompositions; the conjecture may fail or require different arguments for non-standard decompositions.

C3one line summary

The paper proves that a conjecture on double shortcuts holds for standard hypercube decompositions of Bruhat intervals, advancing the Combinatorial Invariance Conjecture for Kazhdan-Lusztig polynomials.

References

17 extracted · 17 resolved · 0 Pith anchors

[1] G.T. Barkley, C. Gaetz,Combinatorial invariance for elementary intervals, Math. Ann.392(2025), 3299–3317 2025

[2] G.T. Barkley, C. Gaetz, T. Lam,Combinatorial invariance for the coefficient ofqin Kazhdan-Lusztig polynomials, arXiv:2601.07793 [math.CO]

[3] A.Björner, F.Brenti,Combinatorics of Coxeter Groups, GraduateTextsinMathematics,231, Springer- Verlag, New York, 2005 2005

[4] C. Blundell, L. Buesing, A. Davies, P. Veli˘ cković, G. Williamson,Towards combinatorial invariance for Kazhdan-Lusztig polynomials, Represent. Theory26(2022), 1145-1191 2022

[5] F.Brenti,A combinatorial formula for Kazhdan-Lusztig polynomials, Invent.Math.118(1994), 371-394 1994

Receipt and verification

First computed	2026-05-18T02:44:48.986932Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

daede5ec01e17838b42877a1422a0b59139f6b332fbb13406fe28209e73acb02

Aliases

arxiv: 2605.13304 · arxiv_version: 2605.13304v1 · doi: 10.48550/arxiv.2605.13304 · pith_short_12: 3LW6L3AB4F4D · pith_short_16: 3LW6L3AB4F4DRNBI · pith_short_8: 3LW6L3AB

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/3LW6L3AB4F4DRNBIO6QUEKQLLE \
  | 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: daede5ec01e17838b42877a1422a0b59139f6b332fbb13406fe28209e73acb02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d6d3655996af036fdeac50f4a0d4108da3e9b772e50b9290c948951a5a868a1",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-13T10:18:10Z",
    "title_canon_sha256": "3c296c6605b829d5798f2ebf705e8a39468c9848c203d2cf496035fa6a52b4f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13304",
    "kind": "arxiv",
    "version": 1
  }
}