## Applications of Group Theory to CombinatoricsApplications of Group Theory to Combinatorics contains 11 survey papers from international experts in combinatorics, group theory and combinatorial topology. The contributions cover topics from quite a diverse spectrum, such as design theory, Belyi functions, group theory, transitive graphs, regular maps, and Hurwitz problems, and present the state |

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### Contents

1 | |

Automorphism groups of Cayley digraphs | 13 |

Symmetrical covers decompositions and factorisations of graphs | 27 |

Complete bipartite maps factorisable groups and generalised Fermat curves | 43 |

Separability properties of groups | 59 |

Coverings enumeration and Hurwitz problems | 71 |

Combinatorial facets of Hurwitz numbers | 109 |

Groups and designs | 133 |

Injectivity radius of triangle group representations with application to regular embeddings of hypermaps | 147 |

Genus parameters and sizings of groups | 155 |

Examples properties and applications | 161 |

181 | |

Back cover | 183 |

### Other editions - View all

Applications of Group Theory to Combinatorics Jack Koolen,Jin Ho Kwak,Ming-Yao Xu No preview available - 2008 |

### Common terms and phrases

abelian action acts algebraic Applications automorphism groups Belyi function block branched called Cayley graphs classes combinatorial complete computational connected consider Construction contains corresponding coverings curves cycles cyclic decomposition defined definition denote designs determined digraphs directed edge elements enumeration epimorphism equations equivalent example exists face fact factorisation finite finite group fixed formula function fundamental group genus given gives group G Hence Hurwitz numbers hypermap induced infinite integer Isoc isomorphic known Kwak Lemma Let G linear London Math Mathematics natural non-orientable normal Note obtained operator orbits orientable pair partition permutation points polynomial positive possible prime primitive problem proof properties proved ramification regular regular embeddings representation represented respectively result Series simple groups space subgroup surface symmetric Theorem theory transitive University valency values vertex vertices