Pith Number

pith:WHRCPAIU

pith:2026:WHRCPAIU5CW6XSLXS25H77LIIX

not attested not anchored not stored refs pending

Rook theory, normal ordering in the $q$-deformed Ore algebra and the polynomial generalization

Matthias Schork

Normal ordering coefficients in the q-deformed Ore algebra equal mixed rook and file placement numbers on the staircase and Laguerre boards.

arxiv:2605.09683 v2 · 2026-05-10 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WHRCPAIU5CW6XSLXS25H77LIIX}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

The q-deformed Ore-Stirling numbers (resp., q-deformed Ore-Lah numbers) are given as mixed placement numbers of rooks and files on the staircase board (resp., Laguerre board).

C2weakest assumption

That the algebraic normal-ordering coefficients admit a direct, weight-preserving bijection with the mixed rook-file placements on the named boards, allowing recurrence relations to be read off combinatorially.

C3one line summary

q-deformed Ore-Stirling numbers count mixed rook-file placements on staircase boards and q-deformed Ore-Lah numbers do the same on Laguerre boards, with the approach extended to polynomial commutation relations XY - qYX = f(Y).

Receipt and verification

First computed	2026-05-20T00:04:35.214788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1e2278114e8adebc97796ba7ffd6845c099f05c65188deb6b15ef028fc9ce46

Aliases

arxiv: 2605.09683 · arxiv_version: 2605.09683v2 · doi: 10.48550/arxiv.2605.09683 · pith_short_12: WHRCPAIU5CW6 · pith_short_16: WHRCPAIU5CW6XSLX · pith_short_8: WHRCPAIU

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/WHRCPAIU5CW6XSLXS25H77LIIX \
  | 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: b1e2278114e8adebc97796ba7ffd6845c099f05c65188deb6b15ef028fc9ce46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4b158e9007f2ce964171bf5983a951f7583aa73db62fa607ce5ae48f8fdd552",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-10T18:04:17Z",
    "title_canon_sha256": "aadb4072460cf2a486ddc99093418938ef6ae8188faa3457aca1a84ebf9a31a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09683",
    "kind": "arxiv",
    "version": 2
  }
}