{
  "id": "1911.13297",
  "version": "v1",
  "published": "2019-11-29T18:55:23.000Z",
  "updated": "2019-11-29T18:55:23.000Z",
  "title": "On the Strength of Chromatic Symmetric Homology for graphs",
  "authors": [
    "Alex Chandler",
    "Radmila Sazdanovic",
    "Salvatore Stella",
    "Martha Yip"
  ],
  "comment": "35 pages, 6 figures",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "In this paper, we investigate the strength of chromatic symmetric homology as a graph invariant. Chromatic symmetric homology is a lift of the chromatic symmetric function for graphs to a homological setting, and its Frobenius characteristic is a q,t generalization of the chromatic symmetric function. We exhibit three pairs of graphs where each pair has the same chromatic symmetric function but distinct homology. We also show that integral chromatic symmetric homology contains torsion, and based on computations, conjecture that Z_2-torsion in bigrading (1,0) detects nonplanarity in the graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-29T18:55:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C31",
      "05E05",
      "05E10",
      "18G35",
      "55N91"
    ],
    "keywords": [
      "chromatic symmetric function",
      "integral chromatic symmetric homology contains",
      "chromatic symmetric homology contains torsion",
      "graph invariant",
      "detects nonplanarity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}