Applications of group theory to combinatorics

Jack Koolen, Jin Ho Kwak, Ming-Yao Xu0415471842, 9780415471848, 9780203885765

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.

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Table of contents :
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