{
  "id": "2412.18598",
  "version": "v1",
  "published": "2024-12-24T18:54:02.000Z",
  "updated": "2024-12-24T18:54:02.000Z",
  "title": "Relative sizes of iterated sumsets",
  "authors": [
    "Noah Kravitz"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $hA$ denote the $h$-fold sumset of a subset $A$ of an abelian group. Nathanson asked if there exist finite sets $A,B \\subseteq \\mathbb{Z}$ and natural numbers $h_1<h_2<h_3$ such that $|h_1A|<|h_1B|$, $|h_2B|<|h_2A|$, and $|h_3A|<|h_3B|$. We answer this question in the affirmative and establish a generalization with arbitrarily many sets and arbitrarily many values of $h$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-24T18:54:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "iterated sumsets",
      "relative sizes",
      "fold sumset",
      "abelian group",
      "finite sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}