{
  "id": "1910.08872",
  "version": "v1",
  "published": "2019-10-20T01:43:02.000Z",
  "updated": "2019-10-20T01:43:02.000Z",
  "title": "Principal specializations of Schubert polynomials and pattern containment",
  "authors": [
    "Yibo Gao"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that the principal specialization of the Schubert polynomial at $w$ is bounded below by $1+p_{132}(w)+p_{1432}(w)$ where $p_u(w)$ is the number of occurrences of the pattern $u$ in $w$, strengthening a previous result by A. Weigandt. We then make a conjecture relating the principal specialization of Schubert polynomials to pattern containment. Finally, we characterize permutations $w$ whose RC-graphs are connected by simple ladder moves via pattern avoidance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-20T01:43:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schubert polynomial",
      "principal specialization",
      "pattern containment",
      "simple ladder moves",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}