05416 - Applications of Group Theory to Combinatorics [Koolen-Kwak-Xu].pdf

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APPLICATIONS OF GROUP THEORY TO COMBINATORICS
SELECTED PAPERS FROM THE C
OM2
M
A
C CONFERENCE ON APPLICATIONS OF
GROUP THEORY TO COMBINATORICS, POHANG, KOREA, 9–12 JULY 2007
Applications of Group Theory
to Combinatorics
Editors
Jack Koolen
Department of Mathematics, Pohang University of Science
and Technology, Pohang 790–784, Korea
Jin Ho Kwak
Department of Mathematics, Pohang University of Science
and Technology, Pohang 790–784, Korea
Ming-Yao Xu
Department of Mathematics, Peking University, Beijing 100891, P.R. China
Supported by Com
2
MaC-KOSEF, Korea
CRC Press/Balkema is an imprint of the Taylor & Francis Group, an informa business
© 2008 Taylor & Francis Group, London, UK
Typeset by Vikatan Publishing Solutions (P) Ltd., Chennai, India
Printed and bound in Great Britain by Anthony Rowe (A CPI-group Company),
Chippenham, Wiltshire
All rights reserved. No part of this publication or the information contained herein may be repro-
duced, stored in a retrieval system, or transmitted in any form or by any means, electronic,
mechanical, by photocopying, recording or otherwise, without written prior permission from the
publisher.
Although all care is taken to ensure integrity and the quality of this publication and the information
herein, no responsibility is assumed by the publishers nor the author for any damage to the property
or persons as a result of operation or use of this publication and/or the information contained herein.
Published by: CRC Press/Balkema
P.O. Box 447, 2300 AK Leiden, The Netherlands
e-mail: Pub.NL@taylorandfrancis.com
www.crcpress.com – www.taylorandfrancis.co.uk – www.balkema.nl
ISBN: 978-0-415-47184-8 (Hardback)
ISBN: 978-0-203-88576-5 (ebook)
Applications of Group Theory to Combinatorics - Koolen, Kwak & Xu (eds)
© 2008 Taylor & Francis Group, London, ISBN 978-0-415-47184-8
Table of Contents
Foreword
About the editors
VII
IX
Combinatorial and computational group-theoretic methods in the
study of graphs, maps and polytopes with maximal symmetry
M. Conder
Automorphism groups of Cayley digraphs
Y.-Q. Feng, Z.-P Lu & M.-Y. Xu
.
Symmetrical covers, decompositions and factorisations of graphs
M. Guidici, C.H. Li & C.E. Praeger
Complete bipartite maps, factorisable groups and generalised Fermat curves
G.A. Jones
Separability properties of groups
G. Kim & C.Y. Tang
Coverings, enumeration and Hurwitz problems
J.H. Kwak, J. Lee & A. Mednykh
Combinatorial facets of Hurwitz numbers
S.K. Lando
Groups and designs
H. Li
Injectivity radius of triangle group representations, with application
to regular embeddings of hypermaps
M. Maˇ aj, J. Širᡠ& M. Ipolyiová
c
n
Genus parameters and sizings of groups
T.W. Tucker
Belyi functions: Examples, properties and applications
A.K. Zvonkin
1
13
27
43
59
71
109
133
147
155
161
Author index
181
V

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