Pith Number

pith:IPZENYRD

pith:2008:IPZENYRDK4CV5NPGBGQUV42LJ2

not attested not anchored not stored refs pending

On Combinatorial Formulas for Macdonald Polynomials

Cristian Lenart

arxiv:0804.4716 v1 · 2008-04-30 · math.CO · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IPZENYRDK4CV5NPGBGQUV42LJ2}

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.

Cited by

1 paper in Pith

Formulas for Koornwinder polynomials

Receipt and verification

First computed	2026-07-04T15:11:15.269119Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43f246e22357055eb5e609a14af34b4e8b7eff4560f39a61c9d3f6747e02ab0e

Aliases

arxiv: 0804.4716 · arxiv_version: 0804.4716v1 · doi: 10.48550/arxiv.0804.4716 · pith_short_12: IPZENYRDK4CV · pith_short_16: IPZENYRDK4CV5NPG · pith_short_8: IPZENYRD

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/IPZENYRDK4CV5NPGBGQUV42LJ2 \
  | 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: 43f246e22357055eb5e609a14af34b4e8b7eff4560f39a61c9d3f6747e02ab0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5064e9e02e703da4e71485a2ef4d32cf898dc1d984a4436dcad655fe737f022",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2008-04-30T13:15:00Z",
    "title_canon_sha256": "e906931b87a9e9505e0da75a9fa9ff1f2036a414733ae9e9c7c11ca6b47cb660"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0804.4716",
    "kind": "arxiv",
    "version": 1
  }
}