{
  "id": "1603.09744",
  "version": "v1",
  "published": "2016-03-31T19:57:20.000Z",
  "updated": "2016-03-31T19:57:20.000Z",
  "title": "Schubert polynomials, slide polynomials, Stanley symmetric functions and quasi-Yamanouchi pipe dreams",
  "authors": [
    "Sami Assaf",
    "Dominic Searles"
  ],
  "comment": "28 pages",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "We introduce two new bases for polynomials that lift monomial and fundamental quasisymmetric functions to the full polynomial ring. By defining a new condition on pipe dreams, called quasi-Yamanouchi, we give a positive combinatorial rule for expanding Schubert polynomials into these new bases that parallels the expansion of Schur functions into fundamental quasisymmetric functions. As a result, we obtain a refinement of the stable limits of Schubert polynomials to Stanley symmetric functions. We also give combinatorial rules for the positive structure constants of these bases that generalize the quasi-shuffle product and shuffle product, respectively. We use this to give a Littlewood--Richardson rule for expanding a product of Schubert polynomials into fundamental slide polynomials and to give formulas for products of Stanley symmetric functions in terms of Schubert structure constants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-31T19:57:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "14N15",
      "05E05"
    ],
    "keywords": [
      "stanley symmetric functions",
      "schubert polynomials",
      "quasi-yamanouchi pipe dreams",
      "slide polynomials",
      "fundamental quasisymmetric functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160309744A"
    }
  }
}