{
  "id": "1909.10109",
  "version": "v1",
  "published": "2019-09-23T01:03:29.000Z",
  "updated": "2019-09-23T01:03:29.000Z",
  "title": "Subset Parking Functions",
  "authors": [
    "Sam Spiro"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A parking function $(c_1,\\ldots,c_n)$ can be viewed as having $n$ cars trying to park on a one-way street with $n$ parking spots, where car $i$ tries to park in spot $c_i$, and otherwise he parks in the leftmost available spot after $c_i$. Another way to view this is that each car has a set $C_i$ of \"acceptable\" parking spots, namely $C_i=[c_i,n]$, and that each car tries to park in the leftmost available spot that they find acceptable. Motivated by this, we define a subset parking function $(C_1,\\ldots,C_n)$, with each $C_i$ a subset of $\\{1,\\ldots,n\\}$, by having the $i$th car try to park in the leftmost available element of $C_i$. We further generalize this idea by restricting our sets to be of size $k$, intervals, and intervals of length $k$. In each of these cases we provide formulas for the number of such parking functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-23T01:03:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A19"
    ],
    "keywords": [
      "subset parking function",
      "parking spots",
      "car tries",
      "one-way street",
      "th car"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}