{
  "id": "2109.13637",
  "version": "v3",
  "published": "2021-09-28T11:52:12.000Z",
  "updated": "2022-03-17T11:06:16.000Z",
  "title": "The direct sum of $q$-matroids",
  "authors": [
    "Michela Ceria",
    "Relinde Jurrius"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For classical matroid, the direct sum is one of the most straightforward methods to make a new matroid out of existing ones. This paper defines a direct sum for $q$-matroids, the $q$-analogue of matroids. This is a lot less straightforward than in the classical case, as we will try to convince the reader. With the use of $q$-polymatroids and the $q$-analogue of matroid union we come to a definition of the direct sum of $q$-matroids. As a motivation for this definition, we show it has some desirable properties.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-03-17T11:06:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "05A30"
    ],
    "keywords": [
      "direct sum",
      "paper defines",
      "matroid union",
      "definition",
      "classical matroid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}