Symmetries in Graphs, Maps, and Polytopes

Name: Symmetries in Graphs, Maps, and Polytopes | 5th SIGMAP Workshop, West Malvern, UK, July 2014
Brand: Springer
Price: 149.79 EUR
Availability: OnlineOnly

5th SIGMAP Workshop, West Malvern, UK, July 2014

Jozef Sirán Robert Jajcay(Herausgeber*in)

Springer (Verlag)

Erschienen am 26. März 2016

X, 332 Seiten

E-Book

PDF mit Wasserzeichen-DRM

Systemvoraussetzungen

978-3-319-30451-9 (ISBN)

149,79 €inkl. 7% MwSt.

Systemvoraussetzungen

für PDF mit Wasserzeichen-DRM

E-Book Einzellizenz

Als Download verfügbar

Beschreibung

Weitere Details

Weitere Ausgaben

Inhalt

Intro
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 Codes
4 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 Introduction
2 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 Hypermaps
8.3 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'enfants
1 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 G-Dessins
6.3 G-Objects in mathfrakSetsxy
6.4 A Complete Example
Cyclic Dessins
7 Concluding Comments
References
Discrete Groups and Surface Automorphisms: A Theorem of A.M. Macbeath
1 Introduction
2 Hurwitz's Theorem Revisited
3 Automorphisms and Geometry in Three Dimensional Hyperbolic Space
References
Isometric Point-Circle Configurations on Surfaces from Uniform Maps
1 Introduction
2 Constructing Configurations of Points and Isometric Circles on Surfaces
3 Point-Circle Configurations from Some Classical Regular Maps
3.1 The Bolza Curve
3.2 Klein's Quartic
3.3 Bring's Curve
4 Pentagonal Geometries as Point-Circle Configurations from Moore Graphs
5 Point-Circle Configurations on p-gonal Surfaces with Two Cyclic p-gonal Morphisms
References
Dessins, Their Delta-Matroids and Partial Duals
1 Introduction
2 Dessins and Bipartite Maps
2.1 A Permutation Representation of Dessins
3 Belyi's Theorem and the Galois Action on Dessins
3.1 Galois Action on Dessins
3.2 Galois Invariants
4 Matroids and Delta-Matroids
4.1 Delta-Matroids
5 Galois Action on the Delta-Matroids of Maps
5.1 Trivial Delta-Matroidal Galois Invariants
5.2 Self-Duality of Maps and Matroids
6 Partial Duals and Twists of Delta-Matroids
6.1 Partial Duals, Delta-Matroids and the Galois Action
7 Maps, Their Partial Duals and Tropical Curves
References
Faithful Embeddings of Planar Graphs on Orientable Closed Surfaces
1 Introduction
2 Faithful Rotation Schemes
3 The 3-Regular Case
4 The 4-Regular Case
5 Conclusion
References
The Higher Dimensional Hemicuboctahedron
1 Introduction
2 Regular Polytopes
3 2-orbit Polytopes
4 The Higher Dimensional Hemicuboctahedron
5 Conclusions
References
Groups of Order at Most 6,000 Generated by Two Elements, One of Which Is an Involution, and Related Structures
1 Introduction
2 Constructing the Census of Small (2,*)-Groups
2.1 Using a Database of Small Groups
2.2 Using the Magma LowIndexNormalSubgroups Algorithm
2.3 Using Group Extensions
3 Proof of Theorem 2
4 (2,*)-Groups and Graphs
4.1 Cubic Cayley Graphs
4.2 Arc-Transitive Digraphs of Out-Valency Two
5 (2,*)-groups and Maps
5.1 Monodromy Groups of Maps
5.2 Oriented Rotary Maps
5.3 Regular Maps
References
Even-Integer Continued Fractions and the Farey Tree
1 Introduction
2 Infinite Continued Fractions
3 Representing Real Numbers by Even-Integer Continued Fractions
4 Serret's Theorem on Continued Fractions
5 An Alternative Characterisation of Convergents of Even-Integer Continued Fractions
6 Approximating Irrationals by Rationals
7 Concluding Remark
References
Triangle Groups and Maps
1 Triangle Groups
2 Some Personal History
3 Basic Concepts
4 Belyi's Theorem
5 Other Triangle Groups
6 Klein Surfaces and Real Belyi Functions
7 Hypermaps
8 Triangle Groups with Infinite Periods
9 Away from Triangle Groups
References
Nilpotent Symmetric Dessins of Class Two
1 Introduction
2 Algebraic Dessins
3 External Symmetries
4 Nilpotent Regular Dessins
5 Simple Symmetric p-Dessins of Class Two
6 Symmetric p-dessins of Class Two with Multiple Edges
References

Inhalt (PDF)

Systemvoraussetzungen

Als PDF speichern Als Link merken