LEADER 06590nam 22007815 450 001 9910254061903321 005 20200629224659.0 010 $a3-319-30451-8 024 7 $a10.1007/978-3-319-30451-9 035 $a(CKB)3710000000621644 035 $a(EBL)4459554 035 $a(SSID)ssj0001654172 035 $a(PQKBManifestationID)16433427 035 $a(PQKBTitleCode)TC0001654172 035 $a(PQKBWorkID)14983007 035 $a(PQKB)10420692 035 $a(DE-He213)978-3-319-30451-9 035 $a(MiAaPQ)EBC4459554 035 $a(PPN)192773364 035 $a(EXLCZ)993710000000621644 100 $a20160326d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSymmetries in Graphs, Maps, and Polytopes $e5th SIGMAP Workshop, West Malvern, UK, July 2014 /$fedited by Jozef ?irá?, Robert Jajcay 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (330 p.) 225 1 $aSpringer Proceedings in Mathematics & Statistics,$x2194-1009 ;$v159 300 $aDescription based upon print version of record. 311 $a3-319-30449-6 320 $aIncludes bibliographical references. 327 $aPreface; 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) 327 $a3 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; Mo?bius Inversion in Suzuki Groups and Enumeration of Regular Objects 327 $a1 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 Mo?bius 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 327 $a8.2 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 327 $aThe Grothendieck-Teichmu?ller 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 327 $a6.2 ?-Dessins 330 $aThis volume contains seventeen of the best papers delivered at the SIGMAP Workshop 2014, representing the most recent advances in the field of symmetries of discrete objects and structures, with a particular emphasis on connections between maps, Riemann surfaces and dessins d?enfant. Providing the global community of researchers in the field with the opportunity to gather, converse and present their newest findings and advances, the Symmetries In Graphs, Maps, and Polytopes Workshop 2014 was the fifth in a series of workshops. The initial workshop, organized by Steve Wilson in Flagstaff, Arizona, in 1998, was followed in 2002 and 2006 by two meetings held in Aveiro, Portugal, organized by Antonio Breda d?Azevedo, and a fourth workshop held in Oaxaca, Mexico, organized by Isabel Hubard in 2010. This book should appeal to both specialists and those seeking a broad overview of what is happening in the area of symmetries of discrete objects and structures. 410 0$aSpringer Proceedings in Mathematics & Statistics,$x2194-1009 ;$v159 606 $aGraph theory 606 $aAlgebra 606 $aField theory (Physics) 606 $aTopological groups 606 $aLie groups 606 $aGraph Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M29020 606 $aField Theory and Polynomials$3https://scigraph.springernature.com/ontologies/product-market-codes/M11051 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 615 0$aGraph theory. 615 0$aAlgebra. 615 0$aField theory (Physics). 615 0$aTopological groups. 615 0$aLie groups. 615 14$aGraph Theory. 615 24$aField Theory and Polynomials. 615 24$aTopological Groups, Lie Groups. 676 $a510 702 $a?irá?$b Jozef$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aJajcay$b Robert$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254061903321 996 $aSymmetries in graphs, maps, and polytopes$91523668 997 $aUNINA