{
  "id": "1605.02307",
  "version": "v1",
  "published": "2016-05-08T10:56:53.000Z",
  "updated": "2016-05-08T10:56:53.000Z",
  "title": "Combinatorial analysis of growth models for series-parallel networks",
  "authors": [
    "Markus Kuba",
    "Alois Panholzer"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We give combinatorial descriptions of two stochastic growth models for series-parallel networks introduced by Hosam Mahmoud by encoding the growth process via recursive tree structures. Using decompositions of the tree structures and applying analytic combinatorics methods allows a study of quantities in the corresponding series-parallel networks. For both models we obtain limiting distribution results for the degree of the poles and the length of a random source-to-sink path, and furthermore we get asymptotic results for the expected number of source-to-sink paths.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-08T10:56:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combinatorial analysis",
      "tree structures",
      "applying analytic combinatorics methods",
      "random source-to-sink path",
      "stochastic growth models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}