{
  "id": "1804.05513",
  "version": "v1",
  "published": "2018-04-16T06:14:56.000Z",
  "updated": "2018-04-16T06:14:56.000Z",
  "title": "A Tight Bound for Hypergraph Regularity II",
  "authors": [
    "Guy Moshkovitz",
    "Asaf Shapira"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The hypergraph regularity lemma -- the extension of Szemer\\'edi's graph regularity lemma to the setting of $k$-uniform hypergraphs -- is one of the most celebrated combinatorial results obtained in the past decade. By now there are several (very different) proofs of this lemma, obtained by Gowers, by Nagle-R\\\"odl-Schacht-Skokan and by Tao. Unfortunately, what all these proofs have in common is that they yield regular partitions whose order is given by the $k$-th Ackermann function. In a recent paper we have shown that these bounds are unavoidable for $3$-uniform hypergraphs. In this paper we extend this result by showing that such Ackermann-type bounds are unavoidable for every $k \\ge 2$, thus confirming a prediction of Tao.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-16T06:14:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tight bound",
      "szemeredis graph regularity lemma",
      "uniform hypergraphs",
      "yield regular partitions",
      "hypergraph regularity lemma"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}