Table Of ContentSpringer Proceedings in Mathematics & Statistics
Jozef Širáň
Robert Jajcay Editors
Symmetries in
Graphs, Maps,
and Polytopes
5th SIGMAP Workshop, West Malvern,
UK, July 2014
Springer Proceedings in Mathematics & Statistics
Volume 159
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Š áň
Jozef ir Robert Jajcay
(cid:129)
Editors
Symmetries in Graphs,
Maps, and Polytopes
5th SIGMAP Workshop,
West Malvern, UK, July 2014
123
Editors
JozefŠiráň RobertJajcay
TheOpen University Comenius University
MiltonKeynes Bratislava
UK Slovakia
ISSN 2194-1009 ISSN 2194-1017 (electronic)
SpringerProceedings in Mathematics& Statistics
ISBN978-3-319-30449-6 ISBN978-3-319-30451-9 (eBook)
DOI 10.1007/978-3-319-30451-9
LibraryofCongressControlNumber:2016934436
MathematicsSubjectClassification: 05E15,05E18,05C25,05C10,22E45
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Preface
TheSymmetriesInGraphs,Maps,AndPolytopesWorkshop2014wasthefifthina
seriesofworkshops,thefirstofwhichwasorganizedbySteveWilsoninFlagstaff,
Arizona, in 1998, under the acronym SIGMAC (with the original ‘C’ standing for
Complexes).Theinitialworkshopwasfollowedin2002and2006bytwomeetings
held in Aveiro, Portugal, organized by Antonio Breda d’Azevedo, and the fourth
workshop,thefirstunderthenameSIGMAP,heldinOaxaca,Mexico,organizedby
Isabel Hubard in 2010. The aim of the workshops is to give the worldwide com-
munity of researchers in symmetries of discrete objects and structures the oppor-
tunity to gather together, exchange information and present their newest findings
and advances.
The SIGMAP 2014 Workshop took place during 7–11 July 2014, in the idyllic
environmentoftheELIMConferenceCentreinthebeautifulareaofMalvern,UK.
It brought together a total of 62 researchers including a number of Ph.D. students.
The list of invited plenary lecturers consisted of:
(cid:129) Marston Conder, University of Auckland, New Zealand;
(cid:129) Shaofei Du, Capital Normal University, Beijing, China;
(cid:129) Gareth Jones, University of Southampton, UK;
(cid:129) Roman Nedela, Matej Bel University, Slovakia;
(cid:129) Primož Potočnik, University of Ljubljana, Slovenia;
(cid:129) David Singerman, University of Southampton, UK;
(cid:129) Asia Ivic Weiss, York University, Toronto, Canada;
(cid:129) Jürgen Wolfart, J.W. Goethe University, Frankfurt, Germany.
The emphasis of the scientific program was on connections between maps,
Riemann surfaces and dessins d’enfants. Gareth Jones, David Singerman and
Jürgen Wolfart jointly delivered a mini-course on these connections. Beside the
mini-course, the daily program consisted of plenary lectures, 34 contributed paper
presentations and many informal discussions held in a collegial and encouraging
atmosphere.EverybodymerrilyjoinedincongratulatingJozefŠiráňontheoccasion
v
vi Preface
of his 60th birthday. The Wednesday conference trip took us to the Worcester
Cathedral and Library and included a short organ recital.
Allparticipantsaretobethankedfortheirvaluablecontributionsandformaking
SIGMAP 2014 a successful and memorable event. This volume contains 17
selectedpapersbasedonthetalksdeliveredattheworkshop,anditrepresentsonly
a part of the workshop’s rich scientific program. Despite that, it is representative
of the variety of topics considered and the interactions between them.
Milton Keynes Jozef Širáň
Bratislava Robert Jajcay
December 2015
Acknowledgements
The organizer gratefully acknowledges support from a Conference Grant from the
London Mathematical Society which enabled to cover accommodation and sub-
sistence for the non-UK invited speakers, as well as support from the British
Combinatorial Committee covering accommodation and subsistence for the
UK-based invited speakers. The Open University is to be thanked for providing
technical and organizational support.
We also wish to thank all our anonymous referees for their selfless and timely
cooperation, without which the publication of these proceedings would be
impossible.
vii
Contents
Powers of Skew-Morphisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Martin Bachratý and Robert Jajcay
Census of Quadrangle Groups Inclusions. . . . . . . . . . . . . . . . . . . . . . . 27
António Breda d'Azevedo, Domenico A. Catalano, Ján Karabáš
and Roman Nedela
Some Unexpected Consequences of Symmetry Computations . . . . . . . . 71
Marston D.E. Conder
A 3D Spinorial View of 4D Exceptional Phenomena. . . . . . . . . . . . . . . 81
Pierre-Philippe Dechant
Möbius Inversion in Suzuki Groups and Enumeration
of Regular Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Martin Downs and Gareth A. Jones
More on Strongly Real Beauville Groups. . . . . . . . . . . . . . . . . . . . . . . 129
Ben Fairbairn
On Pentagonal Geometries with Block Size 3, 4 or 5. . . . . . . . . . . . . . . 147
Terry S. Griggs and Klara Stokes
The Grothendieck-Teichmüller Group of a Finite Group
and G-Dessins d’enfants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Pierre Guillot
Discrete Groups and Surface Automorphisms: A Theorem
of A.M. Macbeath. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
W.J. Harvey
Isometric Point-Circle Configurations on Surfaces
from Uniform Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Milagros Izquierdo and Klara Stokes
ix
x Contents
Dessins, Their Delta-Matroids and Partial Duals . . . . . . . . . . . . . . . . . 213
Goran Malić
Faithful Embeddings of Planar Graphs on Orientable
Closed Surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
Seiya Negami
The Higher Dimensional Hemicuboctahedron. . . . . . . . . . . . . . . . . . . . 263
Daniel Pellicer
Groups of Order at Most 6,000 Generated by Two Elements,
One of Which Is an Involution, and Related Structures . . . . . . . . . . . . 273
Primož Potočnik, Pablo Spiga and Gabriel Verret
Even-Integer Continued Fractions and the Farey Tree . . . . . . . . . . . . . 287
Ian Short and Mairi Walker
Triangle Groups and Maps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
David Singerman
Nilpotent Symmetric Dessins of Class Two. . . . . . . . . . . . . . . . . . . . . . 315
Na-Er Wang, Roman Nedela and Kan Hu
