Pith Number

pith:DFKZGSLK

pith:2026:DFKZGSLKPWGXRCBNRG6T6P4KRR

not attested not anchored not stored refs pending

Partition division maps, symmetric functions and positivity

Lilan Dai, Per Alexandersson

A linear map dividing a partition by k sends Schur functions to Schur-positive symmetric functions.

arxiv:2604.25440 v2 · 2026-04-28 · math.CO · math.RT

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\usepackage{pith}
\pithnumber{DFKZGSLKPWGXRCBNRG6T6P4KRR}

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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

✓ 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

We prove that the image of this map is always Schur-positive, meaning it expands in the Schur basis with nonnegative integer coefficients. These coefficients are enumerated by a new family of combinatorial objects, called k-Yamanouchi tableaux.

C2weakest assumption

The linear map is well-defined on the Schur basis and the combinatorial interpretation via k-Yamanouchi tableaux correctly enumerates the coefficients without hidden cancellations or sign issues.

C3one line summary

A new partition-division map on symmetric functions produces Schur-positive outputs enumerated by k-Yamanouchi tableaux.

Receipt and verification

First computed	2026-05-22T01:04:03.389855Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

195593496a7d8d78882d89bd3f3f8a8c60b0e34f4396e6a2f3c8eb9af3acc160

Aliases

arxiv: 2604.25440 · arxiv_version: 2604.25440v2 · doi: 10.48550/arxiv.2604.25440 · pith_short_12: DFKZGSLKPWGX · pith_short_16: DFKZGSLKPWGXRCBN · pith_short_8: DFKZGSLK

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/DFKZGSLKPWGXRCBNRG6T6P4KRR \
  | 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: 195593496a7d8d78882d89bd3f3f8a8c60b0e34f4396e6a2f3c8eb9af3acc160

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb449f8d1f8ec48ff55958a97d5fbace372a6256839db3c1bf7bb883fdce8244",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-04-28T09:49:11Z",
    "title_canon_sha256": "1567b7c1c3857099ccf0676b6da2fdf049367326dca0bc83563798e98561e475"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25440",
    "kind": "arxiv",
    "version": 2
  }
}