Pith Number

pith:QSMLZQ6R

pith:2026:QSMLZQ6RX522REK4VQRZM7W225

not attested not anchored not stored refs resolved

Inhomogeneous $q$-Whittaker polynomials II: ring theorem and positive specializations

Ajeeth Gunna, Damir Yeliussizov

Inhomogeneous q-Whittaker polynomials form a basis for a commutative ring extending the symmetric functions to a subring of its completion.

arxiv:2605.13432 v1 · 2026-05-13 · math.CO

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\pithnumber{QSMLZQ6RX522REK4VQRZM7W225}

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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

inhomogeneous q-Whittaker polynomials (in countably many variables) form a basis of certain commutative ring extending the ring of symmetric functions to a subring of its completion

C2weakest assumption

The inhomogeneous q-Whittaker polynomials are defined such that they simultaneously extend q-Whittaker and stable Grothendieck polynomials while satisfying the algebraic relations needed for the ring to be commutative and for the basis property to hold in the completion.

C3one line summary

Inhomogeneous q-Whittaker polynomials form a basis for an extended commutative ring of symmetric functions and admit positive specializations related to a subset of Macdonald-positive ones, yielding associated probability distributions.

References

22 extracted · 22 resolved · 9 Pith anchors

[1] On a family of symmetric rational functions 2017 · arXiv:1410.0976

[2] Inhomogeneous spinq-Whittaker polynomials.Annales de la Faculté des sciences de Toulouse : Mathématiques, 33(1):1–68, 2024.arXiv:2104.01415 2024

[3] Cambridge Studies in Advanced Mathematics 2016

[4] Spin $q$-Whittaker polynomials 2021 · arXiv:1701.06292

[5] A Littlewood-Richardson rule for the K-theory of Grassmannians 2002 · arXiv:math/0004137

Receipt and verification

First computed	2026-05-18T02:44:47.153483Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8498bcc3d1bf75a8915cac23967edad76f6d656a9ff8f9adcf15b702f36bfd0c

Aliases

arxiv: 2605.13432 · arxiv_version: 2605.13432v1 · doi: 10.48550/arxiv.2605.13432 · pith_short_12: QSMLZQ6RX522 · pith_short_16: QSMLZQ6RX522REK4 · pith_short_8: QSMLZQ6R

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/QSMLZQ6RX522REK4VQRZM7W225 \
  | 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: 8498bcc3d1bf75a8915cac23967edad76f6d656a9ff8f9adcf15b702f36bfd0c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cdc552117f7de080bef663f9e6af6b9fee82e4b695636c456e781ff893fef14e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-13T12:26:20Z",
    "title_canon_sha256": "ea71bb12afc94ef4e8a4a9dcf634eaa3f11908cc68dcf86c9c04453230a6ef35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13432",
    "kind": "arxiv",
    "version": 1
  }
}