Pith Number

pith:EF5T7QSI

pith:2026:EF5T7QSIXRTFV6MXLBSTFP5ZZS

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Strong persistence index and fluctuations in colon powers of monomial ideals

Jonathan Toledo, Mehrdad Nasernejad

Monomial ideals possess a finite strong persistence index after which (I^{ℓ+1} : I) equals I^ℓ for all larger ℓ.

arxiv:2604.11475 v2 · 2026-04-13 · math.AC

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Claims

C1strongest claim

Let I be an ideal in a commutative Noetherian ring R. We say that a positive integer ℓ₀ is the strong persistence index of I if ℓ₀ is the smallest integer such that (I^{ℓ+1} :_R I) = I^ℓ for all ℓ ≥ ℓ₀. The first aim of this paper is to study this notion for monomial ideals.

C2weakest assumption

The definitions assume that the strong persistence index exists (i.e., there is a finite smallest ℓ₀ satisfying the eventual equality) and that fluctuations can be meaningfully detected by checking finitely many exponents a < b < c; this is not justified in the abstract and may require the Noetherian hypothesis or specific properties of monomial ideals.

C3one line summary

The paper defines the strong persistence index and fluctuation phenomena for colon powers of ideals, then investigates both concepts specifically for monomial ideals.

Receipt and verification

First computed	2026-05-25T02:01:19.412041Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

217b3fc248bc665af997586532bfb9cc9af169a80459721be186ee9357786eaf

Aliases

arxiv: 2604.11475 · arxiv_version: 2604.11475v2 · doi: 10.48550/arxiv.2604.11475 · pith_short_12: EF5T7QSIXRTF · pith_short_16: EF5T7QSIXRTFV6MX · pith_short_8: EF5T7QSI

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/EF5T7QSIXRTFV6MXLBSTFP5ZZS \
  | 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: 217b3fc248bc665af997586532bfb9cc9af169a80459721be186ee9357786eaf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66721a8c9ddafaf937dbfd5e52e4ff3fb1740107573fd756140484e95e3c65ae",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2026-04-13T13:45:05Z",
    "title_canon_sha256": "f5a9aa4af8a3bc95c2adbb3a0a0d216f8d8ec4f7a5532c1d4eb610b233bbebfc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.11475",
    "kind": "arxiv",
    "version": 2
  }
}