{
  "annotation_id": "be182f4a-d943-4bda-bfe8-226ca21278b1",
  "date_created": "2026-03-02T18:01:28.659000Z",
  "date_modified": "2026-03-02T18:01:28.659000Z",
  "file_hash": "328459f44beef5f7227ef8dcd28e235e7448cad953a740883e6a5bfa2fb4473e",
  "private": false,
  "record": {
    "abstract": "P. Melvin and H. Morton studied the expansion of the colored Jones polynomial\nof a knot in powers of q-1 and color. They conjectured an upper bound on the\npower of color versus the power of q-1. They also conjectured that the bounding\nline in their expansion generated the inverse Alexander-Conway polynomial.\nThese conjectures were proved by D. Bar-Natan and S. Garoufalidis.\n  We have conjectured that other `lines\u0027 in the Melvin-Morton expansion are\ngenerated by rational functions with integer coefficients whose denominators\nare powers of the Alexander-Conway polynomial. Here we prove this conjecture by\nusing the R-matrix formula for the colored Jones polynomial and presenting the\nuniversal R-matrix as a `perturbed\u0027 Burau matrix.",
    "arxiv_id": "q-alg/9604005",
    "authors": [
      "L. Rozansky"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "The Universal R-Matrix, Burau Representaion and the Melvin-Morton   Expansion of the Colored Jones Polynomial",
    "url": "https://arxiv.org/abs/q-alg/9604005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "31882d57-a315-4961-8fc8-4ff468d952a6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}