{
  "id": "1103.0239",
  "version": "v4",
  "published": "2011-03-01T18:04:46.000Z",
  "updated": "2011-08-12T15:54:17.000Z",
  "title": "Avoiding Colored Partitions of Lengths Two and Three",
  "authors": [
    "Adam M. Goyt",
    "Lara K. Pudwell"
  ],
  "comment": "24 pages, 3 tables, to appear in the Permutation Patterns 2010 Proceedings, a special issue of Pure Mathematics and Applications",
  "categories": [
    "math.CO"
  ],
  "abstract": "Pattern avoidance in the symmetric group $S_n$ has provided a number of useful connections between seemingly unrelated problems from stack-sorting to Schubert varieties. Recent work has generalized these results to $S_n\\wr C_c$, the objects of which can be viewed as \"colored permutations\". Another body of research that has grown from the study of pattern avoidance in permutations is pattern avoidance in $\\Pi_n$, the set of set partitions of $[n]$. Pattern avoidance in set partitions is a generalization of the well-studied notion of noncrossing partitions. Motivated by recent results in pattern avoidance in $S_n \\wr C_c$ we provide a catalog of initial results for pattern avoidance in colored partitions, $\\Pi_n \\wr C_c$. We note that colored set partitions are not a completely new concept. \\emph{Signed} (2-colored) set partitions appear in the work of Bj\\\"{o}rner and Wachs involving the homology of partition lattices. However, we seek to study these objects in a new enumerative context.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-08-12T15:54:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A18"
    ],
    "keywords": [
      "pattern avoidance",
      "avoiding colored partitions",
      "set partitions appear",
      "schubert varieties",
      "initial results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.0239G"
    }
  }
}