Symmetries in Graphs, Maps, and Polytopes : 5th SIGMAP Workshop, West Malvern, UK, July 2014 / edited by Jozef Širáň, Robert Jajcay.

Format:

Book

Conference/Event

Contributor:

Širáň, Jozef., Editor.

Jajcay, Robert., Editor.

Conference Name:

Symmetries In Graphs, Mans, And Polytopes Workshop (5th : 2014 : Malvern, England), issuing body.

Series:

Springer Proceedings in Mathematics & Statistics, 2194-1017 ; 159

Language:

English

Subjects (All):

Graph theory.

Algebraic fields.

Polynomials.

Topological groups.

Lie groups.

Graph Theory.

Field Theory and Polynomials.

Topological Groups and Lie Groups.

Local Subjects:

Graph Theory.

Field Theory and Polynomials.

Topological Groups and Lie Groups.

Physical Description:

1 online resource (330 p.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Language Note:

English

Summary:

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.

Contents:

Preface; Acknowledgements; Contents; Powers of Skew-Morphisms; 1 Introduction; 2 Basic Properties of Skew-Morphisms and Their Relation to Cayley Maps; 3 Generalization of t-Balanced Skew-Morphisms; 4 Powers of Skew-Morphisms; 5 Coset-Preserving Powers; 6 Coset-Preserving Skew-Morphisms of Cyclic Groups; References; Census of Quadrangle Groups Inclusions; 1 Introduction; 2 Generalised Quadrangle Groups and Constellations; 3 How to Read the Census; References; Some Unexpected Consequences of Symmetry Computations; 1 Introduction; 2 Arc-Transitive Cubic Graphs and SL(3,mathbbZ)

3 Sierpinski's Gasket and Binary Gray Codes4 Regular Maps; References; A 3D Spinorial View of 4D Exceptional Phenomena; 1 Introduction; 2 Root Systems and Reflection Groups; 3 Clifford Versor Framework; 4 H4 as a Rotation Rather Than Reflection Group I: From E8; 5 H4 as a Rotation Rather Than Reflection Group II: From H3; 6 The General Construction: Spinor Induction and the 4D Platonic Solids, Trinities and McKay Correspondence; 7 Group and Representation Theory with Clifford Multivectors; 8 Conclusion; References; Möbius Inversion in Suzuki Groups and Enumeration of Regular Objects

1 Introduction2 Categories and Groups; 2.1 Maps, Hypermaps and Groups; 2.2 Reflexibility; 2.3 Covering Spaces; 3 Counting Homomorphisms; 4 The Suzuki Groups and Their Subgroups; 4.1 The Definition of the Suzuki Groups; 4.2 Basic Properties of Suzuki Groups; 4.3 Some Particular Subgroups; 4.4 The Möbius Function of a Suzuki Group; 5 Subgroups H with G (H); 5.1 Maxint Subgroups; 5.2 Maximal Subgroups; 5.3 Point-Stabilisers in Maximal Subgroups; 5.4 Subgroups H of F; 5.5 Subgroups H of Bi; 6 Size of Conjugacy Classes; 7 Calculating Values of muG; 8 Enumerations; 8.1 Orientably Regular Hypermaps

8.2 Regular Hypermaps8.3 Orientably Regular Maps; 8.4 Regular Maps; 8.5 Surface Coverings; 9 The Smallest Simple Suzuki Group; 10 Postscript; References; More on Strongly Real Beauville Groups; 1 Introduction; 2 Preliminaries; 3 The Finite Simple Groups; 4 Characteristically Simple Groups; 5 Almost Simple Groups; 6 The Groups G:langlegrangletimesG:langlegrangle; 7 Abelian and Nilpotent Groups; References; On Pentagonal Geometries with Block Size 3, 4 or 5; 1 Introduction; 2 Constructions; 3 Block Size 3; 4 Block Sizes 4 and 5; 5 The Case r=2k+1; 6 Concluding Remarks; References

The Grothendieck-Teichmüller Group of a Finite Group and G-Dessins d'enfants1 Introduction; 2 Generalities; 2.1 The Group gb; 2.2 The Group gts(G); 2.3 Inverse Limits; 2.4 The Galois Group of mathbbQ; 2.5 p-Groups and Nilpotent Groups; 3 An Elementary Example: Dihedral Groups; 4 The Case of Simple Groups; 4.1 Notation; 4.2 An Action of outgb on pc; 4.3 The Group mathscrS(G); 4.4 Properties of mathscrS(G); 4.5 A Complete Example; 5 Computing Explicitly; 5.1 Computing gts1G; 5.2 Computing sG; 5.3 Simple Groups of Small Order; 5.4 p-Groups; 6 Dessins d'enfants; 6.1 The Category of Dessins

6.2 Γ-Dessins

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

3-319-30451-8