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pith:U2Z4XUTX

pith:2025:U2Z4XUTXVCQINMHXK737ZQBOMJ

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Intersections of sumsets in additive number theory

Melvyn B. Nathanson

In an additive abelian semigroup, the h-fold sumset of the intersection of a strictly decreasing sequence of sets equals the intersection of the h-fold sumsets only under certain conditions on the sequence.

arxiv:2512.23574 v3 · 2025-12-29 · math.NT

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Claims

C1strongest claim

The question is considered: for a strictly decreasing sequence (A_q) with A = intersection A_q, when does hA = intersection hA_q hold for some or all h ≥ 2 in an additive abelian semigroup S.

C2weakest assumption

The sequence (A_q) is strictly decreasing and S is an additive abelian semigroup, with no further restrictions stated on the sets or the semigroup operation.

C3one line summary

Conditions are examined for equality hA = intersection hA_q where A is the intersection of a strictly decreasing sequence of sets A_q in an additive abelian semigroup.

References

13 extracted · 13 resolved · 0 Pith anchors

[1] Erd˝ os and M 1975

[2] J. Fox, N. Kravitz, and S. Zhang, Finer control on relative sizes of iterated sumsets, arXiv: 2506.05691

[3] N. Kravitz, Relative sizes of iterated sumsets, J. Number Theory 272 (2025), 113–128, 2025

[4] M. B. Nathanson, Minimal bases and maximal nonbases in additive number theory, J. Number Theory 6 (1974), 324–333 1974

[5] M. B. Nathanson, Inverse problems for sumset sizes of finite sets of integers, Fibonacci Quar- terly (2025), to appear. arXiv:2411.02365 2025

Formal links

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Cited by

2 papers in Pith

Global Product Intersection Sets in Semigroups

Problems and results on intersections of product sets and sumsets in semigroups

Receipt and verification

First computed	2026-05-17T23:39:00.339791Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6b3cbd277a8a086b0f757f7fcc02e6277bb4d1bd0683b1e22d65b04edcd7659

Aliases

arxiv: 2512.23574 · arxiv_version: 2512.23574v3 · doi: 10.48550/arxiv.2512.23574 · pith_short_12: U2Z4XUTXVCQI · pith_short_16: U2Z4XUTXVCQINMHX · pith_short_8: U2Z4XUTX

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/U2Z4XUTXVCQINMHXK737ZQBOMJ \
  | 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: a6b3cbd277a8a086b0f757f7fcc02e6277bb4d1bd0683b1e22d65b04edcd7659

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21636d60f5edb3b8088596bb178b0ee2892a8533ef700a6401d4b1e8677cd39e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-12-29T16:14:09Z",
    "title_canon_sha256": "fb5ab7ca9fafd129aede5692c31f4ddc360359531aaa64df67cd0e2ccdf7123c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.23574",
    "kind": "arxiv",
    "version": 3
  }
}