{
  "id": "1809.04433",
  "version": "v1",
  "published": "2018-09-10T21:38:28.000Z",
  "updated": "2018-09-10T21:38:28.000Z",
  "title": "Symmetric Function Theory at the Border of A_n and C_n",
  "authors": [
    "Graham Hawkes"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We relate the type $A_n$ and type $C_n$ Stanley symmetric functions, by producing a new symmetric function: Our double Stanley symmetric function gives the type $A$ case at $(\\mathbf{x},\\mathbf{0})$ and gives the type $C$ case at $(\\mathbf{x},\\mathbf{x})$ and is symmetric and Schur positive in general at $(\\mathbf{x}, \\mathbf{y})$ for $\\omega \\in A_n \\subseteq C_n$. In order to produce a Schur expansion for our functions, we make two attempts to generalize Edelman-Greene to signed words. We successfully do this using a \\emph{signed-recording Edelman-Greene} map. However, the dual notion of the \\emph{singed-insertion Edelman-Greene} map appears a difficult task, although its possible existence leaves us with the interesting conjecture of the \\emph{even} and \\emph{odd} Stanley symmetric functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-10T21:38:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric function theory",
      "double stanley symmetric function",
      "schur expansion",
      "dual notion",
      "map appears"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}