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Author : Norman L. Biggs,A. T. White
Publisher : Unknown
Page : 152 pages
File Size : 48,7 Mb
Release : 1979
Category : Combinatorial analysis
ISBN : OCLC:472109769
The subject of this book is the action of permutation groups on sets associated with combinatorial structures.
Author : Norman Biggs,A. T. White
Publisher : Cambridge University Press
Page : 153 pages
File Size : 44,7 Mb
Release : 1979-08-16
Category : Mathematics
ISBN : 9780521222877
The subject of this book is the action of permutation groups on sets associated with combinatorial structures. Each chapter deals with a particular structure: groups, geometries, designs, graphs and maps respectively. A unifying theme for the first four chapters is the construction of finite simple groups. In the fifth chapter, a theory of maps on orientable surfaces is developed within a combinatorial framework. This simplifies and extends the existing literature in the field. The book is designed both as a course text and as a reference book for advanced undergraduate and graduate students. A feature is the set of carefully constructed projects, intended to give the reader a deeper understanding of the subject.
Author : Peter J. Cameron
Publisher : Cambridge University Press
Page : 236 pages
File Size : 55,8 Mb
Release : 1999-02-04
Category : Mathematics
ISBN : 0521653789
This book summarizes recent developments in the study of permutation groups for beginning graduate students.
Author : Meenaxi Bhattacharjee,Dugald Macpherson,Rögnvaldur G. Möller,Peter M. Neumann
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 40,9 Mb
Release : 1998-11-20
Category : Mathematics
ISBN : 3540649654
The book, based on a course of lectures by the authors at the Indian Institute of Technology, Guwahati, covers aspects of infinite permutation groups theory and some related model-theoretic constructions. There is basic background in both group theory and the necessary model theory, and the following topics are covered: transitivity and primitivity; symmetric groups and general linear groups; wreatch products; automorphism groups of various treelike objects; model-theoretic constructions for building structures with rich automorphism groups, the structure and classification of infinite primitive Jordan groups (surveyed); applications and open problems. With many examples and exercises, the book is intended primarily for a beginning graduate student in group theory.
Author : John D. Dixon,Brian Mortimer
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207313
Following the basic ideas, standard constructions and important examples in the theory of permutation groups, the book goes on to develop the combinatorial and group theoretic structure of primitive groups leading to the proof of the pivotal ONan-Scott Theorem which links finite primitive groups with finite simple groups. Special topics covered include the Mathieu groups, multiply transitive groups, and recent work on the subgroups of the infinite symmetric groups. With its many exercises and detailed references to the current literature, this text can serve as an introduction to permutation groups in a course at the graduate or advanced undergraduate level, as well as for self-study.
Author : Cheryl E. Praeger,Csaba Schneider
Publisher : London Mathematical Society Le
Page : 338 pages
File Size : 47,9 Mb
Release : 2018-05-03
Category : Mathematics
ISBN : 9780521675062
Concise introduction to permutation groups, focusing on invariant cartesian decompositions and applications in algebra and combinatorics.
Author : Gregory Butler
Publisher : Springer
Page : 244 pages
File Size : 45,7 Mb
Release : 1991-11-27
Category : Computers
ISBN : 3540549552
This is the first-ever book on computational group theory. It provides extensive and up-to-date coverage of the fundamental algorithms for permutation groups with reference to aspects of combinatorial group theory, soluble groups, and p-groups where appropriate. The book begins with a constructive introduction to group theory and algorithms for computing with small groups, followed by a gradual discussion of the basic ideas of Sims for computing with very large permutation groups, and concludes with algorithms that use group homomorphisms, as in the computation of Sylowsubgroups. No background in group theory is assumed. The emphasis is on the details of the data structures and implementation which makes the algorithms effective when applied to realistic problems. The algorithms are developed hand-in-hand with the theoretical and practical justification.All algorithms are clearly described, examples are given, exercises reinforce understanding, and detailed bibliographical remarks explain the history and context of the work. Much of the later material on homomorphisms, Sylow subgroups, and soluble permutation groups is new.
Author : Peter J. Cameron
Publisher : Cambridge University Press
Page : 172 pages
File Size : 50,7 Mb
Release : 1990-06-29
Category : Mathematics
ISBN : 9780521388368
The study of permutations groups has always been closely associated with that of highly symmetric structures. The objects considered here are countably infinite, but have only finitely many different substructures of any given finite size. This book discusses such structures, their substructures and their automorphism groups using a wide range of techniques.
Author : Andrew Martin William Glass
Publisher : Cambridge University Press
Page : 333 pages
File Size : 53,5 Mb
Release : 1981
Category : Mathematics
ISBN : 9780521241908
As a result of the work of the nineteenth-century mathematician Arthur Cayley, algebraists and geometers have extensively studied permutation of sets. In the special case that the underlying set is linearly ordered, there is a natural subgroup to study, namely the set of permutations that preserves that order. In some senses. these are universal for automorphisms of models of theories. The purpose of this book is to make a thorough, comprehensive examination of these groups of permutations. After providing the initial background Professor Glass develops the general structure theory, emphasizing throughout the geometric and intuitive aspects of the subject. He includes many applications to infinite simple groups, ordered permutation groups and lattice-ordered groups. The streamlined approach will enable the beginning graduate student to reach the frontiers of the subject smoothly and quickly. Indeed much of the material included has never been available in book form before, so this account should also be useful as a reference work for professionals.
Author : Richard Arratia,A. D. Barbour,Simon Tavaré
Publisher : European Mathematical Society
Page : 380 pages
File Size : 54,9 Mb
Release : 2003
Category : Mathematics
ISBN : 3037190000
This book explains similarities in asymptotic behavior as the result of two basic properties shared by the structures: the conditioning relation and the logarithmic condition. The discussion is conducted in the language of probability, enabling the theory to be developed under rather general and explicit conditions; for the finer conclusions, Stein's method emerges as the key ingredient.
Author : Peter Jephson Cameron
Publisher : Unknown
Page : 170 pages
File Size : 53,5 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 110736163X
The study of permutation groups has always been closely associated with that of highly symmetric structures. The objects considered here are countably infinite, but have only finitely many different substructures of any given finite size. They are precisely those structures which are determined by first-order logical axioms together with the assumption of countability. This book concerns such structures, their substructures and their automorphism groups. A wide range of techniques are used: group theory, combinatorics, Baire category and measure among them. The book arose from lectures given at a research symposium and retains their informal style, whilst including as well many recent results from a variety of sources. It concludes with exercises and unsolved research problems.
Author : Peter Jephson Cameron
Publisher : Cambridge University Press
Page : 372 pages
File Size : 47,8 Mb
Release : 1994-10-06
Category : Mathematics
ISBN : 0521457610
Combinatorics is a subject of increasing importance, owing to its links with computer science, statistics and algebra. This is a textbook aimed at second-year undergraduates to beginning graduates. It stresses common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter and also stresses the fact that a constructive or algorithmic proof is more valuable than an existence proof. The book is divided into two parts, the second at a higher level and with a wider range than the first. Historical notes are included which give a wider perspective on the subject. More advanced topics are given as projects and there are a number of exercises, some with solutions given.
Author : D. G. Higman
Publisher : Unknown
Page : 66 pages
File Size : 43,8 Mb
Release : 1972
Category : Combinatorial analysis
ISBN : UOM:39015017308050
Author : L. Lovász
Publisher : Elsevier
Page : 636 pages
File Size : 43,9 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9780080933092
The aim of this book is to introduce a range of combinatorial methods for those who want to apply these methods in the solution of practical and theoretical problems. Various tricks and techniques are taught by means of exercises. Hints are given in a separate section and a third section contains all solutions in detail. A dictionary section gives definitions of the combinatorial notions occurring in the book. Combinatorial Problems and Exercises was first published in 1979. This revised edition has the same basic structure but has been brought up to date with a series of exercises on random walks on graphs and their relations to eigenvalues, expansion properties and electrical resistance. In various chapters the author found lines of thought that have been extended in a natural and significant way in recent years. About 60 new exercises (more counting sub-problems) have been added and several solutions have been simplified.
Author : Philippe Flajolet,Robert Sedgewick
Publisher : Cambridge University Press
Page : 825 pages
File Size : 40,7 Mb
Release : 2009-01-15
Category : Mathematics
ISBN : 9781139477161
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
