Symmetries in Graphs, Maps, and Polytopes: 5th SIGMAP Workshop, West Malvern, UK, July 2014 (Springer Proceedings in Mathematics & Statistics Book 159)

This volume contains seventeen of the best papers delivered at the SIGMAP Workshop 2014, representing the most recent advances in the field of symmetries of discrete objects and structures, with a particular emphasis on connections between maps, Riemann surfaces and dessins d’enfant. Providing the global community of researchers in the field with the opportunity to gather, converse and present their newest findings and advances, the Symmetries In Graphs, Maps, and Polytopes Workshop 2014 was the fifth in a series of workshops. The initial workshop, organized by Steve Wilson in Flagstaff, Arizona, in 1998, was followed in 2002 and 2006 by two meetings held in Aveiro, Portugal, organized by Antonio Breda d’Azevedo, and a fourth workshop held in Oaxaca, Mexico, organized by Isabel Hubard in 2010. This book should appeal to both specialists and those seeking a broad overview of what is happening in the area of symmetries of discrete objects and structures.iv> Front Matter ....Pages i-x Powers of Skew-Morphisms (Martin Bachratý, Robert Jajcay)....Pages 1-25 Census of Quadrangle Groups Inclusions (António Breda d’Azevedo, Domenico A. Catalano, Ján Karabáš, Roman Nedela)....Pages 27-69 Some Unexpected Consequences of Symmetry Computations (Marston D. E. Conder)....Pages 71-79 A 3D Spinorial View of 4D Exceptional Phenomena (Pierre-Philippe Dechant)....Pages 81-95 Möbius Inversion in Suzuki Groups and Enumeration of Regular Objects (Martin Downs, Gareth A. Jones)....Pages 97-127 More on Strongly Real Beauville Groups (Ben Fairbairn)....Pages 129-146 On Pentagonal Geometries with Block Size 3, 4 or 5 (Terry S. Griggs, Klara Stokes)....Pages 147-157 The Grothendieck-Teichmüller Group of a Finite Group and \({\varvec{G}}\)-Dessins d’enfants (Pierre Guillot)....Pages 159-191 Discrete Groups and Surface Automorphisms: A Theorem of A.M. Macbeath (W. J. Harvey)....Pages 193-199 Isometric Point-Circle Configurations on Surfaces from Uniform Maps (Milagros Izquierdo, Klara Stokes)....Pages 201-211 Dessins, Their Delta-Matroids and Partial Duals (Goran Malić)....Pages 213-247 Faithful Embeddings of Planar Graphs on Orientable Closed Surfaces (Seiya Negami)....Pages 249-262 The Higher Dimensional Hemicuboctahedron (Daniel Pellicer)....Pages 263-271 Groups of Order at Most 6,000 Generated by Two Elements, One of Which Is an Involution, and Related Structures (Primož Potočnik, Pablo Spiga, Gabriel Verret)....Pages 273-286 Even-Integer Continued Fractions and the Farey Tree (Ian Short, Mairi Walker)....Pages 287-300 Triangle Groups and Maps (David Singerman)....Pages 301-313 Nilpotent Symmetric Dessins of Class Two (Na-Er Wang, Roman Nedela, Kan Hu)....Pages 315-332 This volume contains seventeen of the best papers delivered at the SIGMAP Workshop 2014, representing the most recent advances in the field of symmetries of discrete objects and structures, with a particular emphasis on connections between maps, Riemann surfaces and dessins d@0394@03C3enfant. Providing the global community of researchers in the field with the opportunity to gather, converse and present their newest findings and advances, the Symmetries In Graphs, Maps, and Polytopes Workshop 2014 was the fifth in a series of workshops. The initial workshop, organized by Steve Wilson in Flagstaff, Arizona, in 1998, was followed in 2002 and 2006 by two meetings held in Aveiro, Portugal, organized by Antonio Breda d@0394@03C3Azevedo, and a fourth workshop held in Oaxaca, Mexico, organized by Isabel Hubard in 2010. This book should appeal to both specialists and those seeking a broad overview of what is happening in the area of symmetries of discrete objects and structures