Pith Number

pith:CCMTX6GK

pith:2026:CCMTX6GKJTQQ3R6ORFBDTZ5V6S

not attested not anchored not stored refs pending

Reciprocals of Subsum Polynomials

Brooke Feigon, Cristina Ballantine, George Beck, Kathrin Maurischat

The sum of reciprocals of subsum polynomials over all partitions of n has arithmetic properties and connections to combinatorial objects.

arxiv:2605.10512 v2 · 2026-05-11 · math.NT · math.CO

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Record completeness

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4 Citations open

5 Replications open

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Claims

C1strongest claim

We introduce the subsum polynomial of a partition λ=(λ1, λ2, …, λk) defined by sp(λ, x)=∏i=1k(1+x^λi). We study the sum of reciprocals of sp(λ, x) over all partitions of n. We prove arithmetic properties of related polynomials and offer connections to other combinatorial objects.

C2weakest assumption

That the sum of reciprocals of the subsum polynomials over partitions of n admits provable arithmetic properties and non-trivial connections to other combinatorial objects.

C3one line summary

Introduces the subsum polynomial sp(λ, x) = product (1 + x^λi) for partitions λ and studies the sum of reciprocals over all partitions of n, proving arithmetic properties and combinatorial connections.

Formal links

2 machine-checked theorem links

Cited by

2 papers in Pith

Reciprocals of Partition Polynomials

Receipt and verification

First computed	2026-06-10T00:08:26.789252Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10993bf8ca4ce10dc7ce894239e7b5f492195706e033ac92072e9ae654ee27cd

Aliases

arxiv: 2605.10512 · arxiv_version: 2605.10512v2 · doi: 10.48550/arxiv.2605.10512 · pith_short_12: CCMTX6GKJTQQ · pith_short_16: CCMTX6GKJTQQ3R6O · pith_short_8: CCMTX6GK

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CCMTX6GKJTQQ3R6ORFBDTZ5V6S \
  | 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: 10993bf8ca4ce10dc7ce894239e7b5f492195706e033ac92072e9ae654ee27cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "892faef929e864ae8b928e99a1a232c5988c188f66bbb6b063960d95326b7934",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-11T13:04:47Z",
    "title_canon_sha256": "eeb17753367e5fec8b0092af91622d892e962ac216c0957fdb759e8270d15ea3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.10512",
    "kind": "arxiv",
    "version": 2
  }
}