Pith Number

pith:YDANYKN5

pith:2026:YDANYKN53FH3OWWOQAXVMKHZNA

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Majorization Inequalities from Logarithmic Convexity

Colin McSwiggen, Siddhartha Sahi

Log-convexity in the indexing partition implies majorization inequalities for Macdonald polynomials, Jack polynomials, and Heckman-Opdam hypergeometric functions.

arxiv:2605.12680 v1 · 2026-05-12 · math.CO · math.RT

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Claims

C1strongest claim

Using log-convexity as a unifying principle, we prove new majorization inequalities for Macdonald polynomials, Jack polynomials and Heckman-Opdam hypergeometric functions, unifying existing results and resolving several open conjectures.

C2weakest assumption

That the specific functions (Macdonald, Jack, Heckman-Opdam) satisfy log-convexity in the indexing partition and that this property is preserved under the operations needed for the inductive arguments.

C3one line summary

Log-convexity implies convexity and thus majorization inequalities for Macdonald polynomials, Jack polynomials, and Heckman-Opdam hypergeometric functions, unifying prior results and resolving open conjectures.

References

31 extracted · 31 resolved · 3 Pith anchors

[1] R. Ait-Haddou and M.-L. Mazure,The fundamental blossoming inequality in Chebyshev spaces–I: Application to Schur functions, Foundations of Computational Mathematics18(2018), 135–158 2018

[2] B. Amri and K. Bedhiafi,A formula for the nonsymmetric Opdam’s hypergeometric function of typeA 2, Journal of Lie Theory27(2017), 309–335 2017

[3] An introduction to Dunkl theory and its analytic aspects 2015 · arXiv:1611.08213

[4] Alexei Borodin and Vadim Gorin,GeneralβJacobi corners process and the Gaussian free field, Communications on Pure and Applied Mathematics68(2015), no. 10, 1774–1844 2015

[5] Hong Chen, Apoorva Khare, and Siddhartha Sahi,Majorization via positivity of Jack and Macdonald polynomial differences, arXiv preprint arXiv:2509.19649 (2025),https://arxiv.org/abs/2509.19649 2025

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Receipt and verification

First computed	2026-05-18T03:09:50.008162Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0c0dc29bdd94fb75ace802f5628f9682d9e75cf66482239f4368f4ad16d224d

Aliases

arxiv: 2605.12680 · arxiv_version: 2605.12680v1 · doi: 10.48550/arxiv.2605.12680 · pith_short_12: YDANYKN53FH3 · pith_short_16: YDANYKN53FH3OWWO · pith_short_8: YDANYKN5

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YDANYKN53FH3OWWOQAXVMKHZNA \
  | 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: c0c0dc29bdd94fb75ace802f5628f9682d9e75cf66482239f4368f4ad16d224d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61080c5063c8833be85b501ef6f168561e1ed95d77ec52cbd2fcfafe38e9d027",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-12T19:30:23Z",
    "title_canon_sha256": "88ba3a9caf37fd46acd7d7d46fbe17448bab0dc64b260466162fc14bff8215c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12680",
    "kind": "arxiv",
    "version": 1
  }
}