{
  "id": "2209.09598",
  "version": "v1",
  "published": "2022-09-20T10:22:13.000Z",
  "updated": "2022-09-20T10:22:13.000Z",
  "title": "Complement Avoidance in Binary Words",
  "authors": [
    "James Currie",
    "Pascal Ochem",
    "Narad Rampersad",
    "Jeffrey Shallit"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "The complement $\\overline{x}$ of a binary word $x$ is obtained by changing each $0$ in $x$ to $1$ and vice versa. We study infinite binary words $\\bf w$ that avoid sufficiently large complementary factors; that is, if $x$ is a factor of $\\bf w$ then $\\overline{x}$ is not a factor of $\\bf w$. In particular, we classify such words according to their critical exponents.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-20T10:22:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complement avoidance",
      "study infinite binary words",
      "avoid sufficiently large complementary factors",
      "vice versa"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}