{
  "id": "2211.07298",
  "version": "v1",
  "published": "2022-11-14T12:20:31.000Z",
  "updated": "2022-11-14T12:20:31.000Z",
  "title": "Effective algebraicity for solutions of systems of functional equations with one catalytic variable",
  "authors": [
    "Hadrien Notarantonio",
    "Sergey Yurkevich"
  ],
  "categories": [
    "math.CO",
    "math.AC",
    "math.CA"
  ],
  "abstract": "We study systems of $n \\geq 1$ discrete differential equations of order $k\\geq1$ in one catalytic variable and provide a constructive and elementary proof of algebraicity of their solutions. This yields effective bounds and a systematic method for computing the minimal polynomials. Our approach is a generalization of the pioneering work by Bousquet-M\\'elou and Jehanne (2006).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-14T12:20:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "functional equations",
      "catalytic variable",
      "effective algebraicity",
      "discrete differential equations",
      "study systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}