Basic Techniques of Combinatorial Theory
Author : Daniel I. A. Cohen
Publisher : John Wiley & Sons
Page : 318 pages
File Size : 44,94 MB
Release : 1978
Category : Mathematics
ISBN :
Author : Daniel I. A. Cohen
Publisher : John Wiley & Sons
Page : 318 pages
File Size : 44,94 MB
Release : 1978
Category : Mathematics
ISBN :
Author : Alexander Mikhalev
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 14,20 MB
Release : 2004
Category : Mathematics
ISBN : 9780387405629
The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20th Century. This book is divided into three fairly independent parts. Part I provides a brief exposition of several classical techniques in combinatorial group theory, namely, methods of Nielsen, Whitehead, and Tietze. Part II contains the main focus of the book. Here the authors show how the aforementioned techniques of combinatorial group theory found their way into affine algebraic geometry, a fascinating area of mathematics that studies polynomials and polynomial mappings. Part III illustrates how ideas from combinatorial group theory contributed to the theory of free algebras. The focus here is on Schreier varieties of algebras (a variety of algebras is said to be Schreier if any subalgebra of a free algebra of this variety is free in the same variety of algebras).
Author : Martin Aigner
Publisher : Springer Science & Business Media
Page : 493 pages
File Size : 41,48 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642591019
This book offers a well-organized, easy-to-follow introduction to combinatorial theory, with examples, notes and exercises. ". . . a very good introduction to combinatorics. This book can warmly be recommended first of all to students interested in combinatorics." Publicationes Mathematicae Debrecen
Author : Sharad S. Sane
Publisher : Hindustan Book Agency
Page : 0 pages
File Size : 36,39 MB
Release : 2013-01-15
Category : Mathematics
ISBN : 9789380250489
This is a basic text on combinatorics that deals with all the three aspects of the discipline: tricks, techniques and theory, and attempts to blend them. The book has several distinctive features. Probability and random variables with their interconnections to permutations are discussed. The theme of parity has been specially included and it covers applications ranging from solving the Nim game to the quadratic reciprocity law. Chapters related to geometry include triangulations and Sperner's theorem, classification of regular polytopes, tilings and an introduction to the Eulcidean Ramsey theory. Material on group actions covers Sylow theory, automorphism groups and a classification of finite subgroups of orthogonal groups. All chapters have a large number of exercises with varying degrees of difficulty, ranging from material suitable for Mathematical Olympiads to research.
Author : Chuan Chong Chen
Publisher : World Scientific
Page : 314 pages
File Size : 20,2 MB
Release : 1992-07-22
Category : Mathematics
ISBN : 981436567X
A textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included.
Author : Philippe Flajolet
Publisher : Cambridge University Press
Page : 825 pages
File Size : 41,47 MB
Release : 2009-01-15
Category : Mathematics
ISBN : 1139477161
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.
Author : Russell Merris
Publisher : John Wiley & Sons
Page : 572 pages
File Size : 17,52 MB
Release : 2003-09-24
Category : Mathematics
ISBN : 047145849X
A mathematical gem–freshly cleaned and polished This book is intended to be used as the text for a first course in combinatorics. the text has been shaped by two goals, namely, to make complex mathematics accessible to students with a wide range of abilities, interests, and motivations; and to create a pedagogical tool, useful to the broad spectrum of instructors who bring a variety of perspectives and expectations to such a course. Features retained from the first edition: Lively and engaging writing style Timely and appropriate examples Numerous well-chosen exercises Flexible modular format Optional sections and appendices Highlights of Second Edition enhancements: Smoothed and polished exposition, with a sharpened focus on key ideas Expanded discussion of linear codes New optional section on algorithms Greatly expanded hints and answers section Many new exercises and examples
Author : Marshall Hall
Publisher : John Wiley & Sons
Page : 464 pages
File Size : 11,42 MB
Release : 1998-07-16
Category : Mathematics
ISBN : 9780471315186
Includes proof of van der Waerden's 1926 conjecture on permanents, Wilson's theorem on asymptotic existence, and other developments in combinatorics since 1967. Also covers coding theory and its important connection with designs, problems of enumeration, and partition. Presents fundamentals in addition to latest advances, with illustrative problems at the end of each chapter. Enlarged appendixes include a longer list of block designs.
Author : Chuan-Chong Chen
Publisher : World Scientific
Page : 314 pages
File Size : 46,99 MB
Release : 1992
Category : Mathematics
ISBN : 9789810211394
A textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included.
Author : Peter Jephson Cameron
Publisher : Cambridge University Press
Page : 372 pages
File Size : 50,51 MB
Release : 1994-10-06
Category : Mathematics
ISBN : 9780521457613
Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra. This textbook stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof. The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics.