{
  "id": "2004.01659",
  "version": "v1",
  "published": "2020-04-03T16:27:50.000Z",
  "updated": "2020-04-03T16:27:50.000Z",
  "title": "Shuffling and $P$-partitions",
  "authors": [
    "Jason Fulman",
    "T. Kyle Petersen"
  ],
  "comment": "19 pages, 4 tables",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "In this survey article, we highlight the direct connection between card shuffling and the functions known as $P$-partitions that come from algebraic combinatorics. While many (but not all) of the results we discuss are known, we give a unified treatment. The key idea is this: the probability of obtaining a permutation $\\pi$ from shelf shuffling is the probability that a random $P$-partition is sorted by $\\pi$, and the probability of obtaining $\\pi$ from riffle shuffling is the probability that a random $P$-partition is sorted by $\\pi^{-1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-03T16:27:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "60C05"
    ],
    "keywords": [
      "probability",
      "algebraic combinatorics",
      "survey article",
      "direct connection",
      "unified treatment"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}