{
  "id": "2012.01329",
  "version": "v1",
  "published": "2020-12-02T16:57:05.000Z",
  "updated": "2020-12-02T16:57:05.000Z",
  "title": "Studies in Additive Number Theory by Circles of Partition",
  "authors": [
    "Theophilus Agama",
    "Berndt Gensel"
  ],
  "comment": "41 pages; submitted to Journal of number theory",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "In this paper we introduce and develop the circle embedding method. This method hinges essentially on a Combinatorial structure which we choose to call circles of partition. We provide applications in the context of problems relating to deciding on the feasibility of partitioning numbers into certain class of integers. In particular, our method allows us to partition any sufficiently large number $n\\in\\mathbb{N}$ into any set $\\mathbb{H}$ with natural density greater than $\\frac{1}{2}$. This possibility could herald an unprecedented progress on class of problems of similar flavour.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-02T16:57:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "additive number theory",
      "natural density greater",
      "circle embedding method",
      "combinatorial structure",
      "sufficiently large number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}