Applications of group theory to combinatorics : selected papers from the Com[superscript 2]MaC Conference on Applications of Group Theory to Combinatorics, Pohang, Korea, 9-12 July 2007

**Applications 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-of-the-art in these areas. **Applications of Group Theory to Combinatorics will be useful in the study of graphs, maps and polytopes having maximal symmetry, and is aimed at researchers in the areas of group theory and combinatorics, graduate students in mathematics, and other specialists who use group theory and combinatorics.**** **Jack Koolen teaches at the Department of Mathematics at Pohang University of Science and Technology, Korea. His main research interests include the interaction of geometry, linear algebra and combinatorics, on which he published 60 papers.** **Jin Ho Kwak is Professor at the Department of Mathematics at Pohang University of Science and Technology, Korea, where he is director of the Combinatorial and Computational Mathematics Center (Com2MaC). He works on combinatorial topology, mainly on covering enumeration related to Hurwitz problems and regular maps on surfaces, and published more than 100 papers in these areas.** **Ming-Yao Xu is Professor in Department of Mathematics at Peking University, China. The focus in his research is in finite group theory and algebraic graph theory. Ming-Yao Xu published over 80 papers on these topics.** Front cover......Page 1 Table of Contents......Page 6 Foreword......Page 8 About the editors......Page 10 Combinatorial and computational group-theoretic methods in the study of graphs, maps and polytopes with maximal symmetry......Page 12 Automorphism groups of Cayley digraphs......Page 24 Symmetrical covers, decompositions and factorisations of graphs......Page 38 Complete bipartite maps, factorisable groups and generalised Fermat curves......Page 54 Separability properties of groups......Page 70 Coverings, enumeration and Hurwitz problems......Page 82 Combinatorial facets of Hurwitz numbers......Page 120 Groups and designs......Page 144 Injectivity radius of triangle group representations, with application to regular embeddings of hypermaps......Page 158 Genus parameters and sizings of groups......Page 166 Belyi functions: Examples, properties and applications......Page 172 Author index......Page 192 Back cover......Page 194 TeX output 2008.06.04:1751 Front cover 1 Table of Contents 6 Foreword 8 About the editors 10 Combinatorial and computational group-theoretic methods in the study of graphs, maps and polytopes with maximal symmetry 12 Automorphism groups of Cayley digraphs 24 Symmetrical covers, decompositions and factorisations of graphs 38 Complete bipartite maps, factorisable groups and generalised Fermat curves 54 Separability properties of groups 70 Coverings, enumeration and Hurwitz problems 82 Combinatorial facets of Hurwitz numbers 120 Groups and designs 144 Injectivity radius of triangle group representations, with application to regular embeddings of hypermaps 158 Genus parameters and sizings of groups 166 Belyi functions: Examples, properties and applications 172 Author index 192 Back cover 194 "Applications 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-of-the-art in these areas. Applications of Group Theory to Combinatorics will be useful in the study of graphs, maps and polytopes having maximal symmetry, and is aimed at researchers in the areas of group theory and combinatorics, graduate students in mathematics, and other specialists who use group theory and combinatorics."--Résumé de l'éditeur

Applications 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

Each paper gives an overview of the current state of the art of the given subject and is aimed at researchers and graduate students who use combinatorics and group theory.-John van Bon, Nieuw Archief voor Wiskunde, December 2011 Editors, Jack Koolen, Jin Ho Kwak, Ming-yao Xu. Includes Bibliographical References.