{
  "id": "2006.14562",
  "version": "v1",
  "published": "2020-06-25T17:06:28.000Z",
  "updated": "2020-06-25T17:06:28.000Z",
  "title": "A new class of minimal asymptotic bases",
  "authors": [
    "Melvyn B. Nathanson"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "A set $A$ of nonnegative integers is an asymptotic basis of order $h$ if every sufficiently large integer can be represented as the sum of $h$ not necessarily distinct elements of $A$. The asymptotic basis $A$ is minimal if removing any element of $A$ destroys every representation of infinitely many integers, and so $A\\setminus \\{a\\}$ is not an asymptotic basis of order $h$ for all $a\\in A$. In this paper, a new class of minimal asymptotic bases is constructed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-25T17:06:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B13",
      "11B05",
      "11B34",
      "11B75"
    ],
    "keywords": [
      "asymptotic basis",
      "minimal asymptotic bases",
      "necessarily distinct elements",
      "sufficiently large integer",
      "nonnegative integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}