Algebraic Combinatorics Via Finite Group Actions
Author | : Adalbert Kerber |
Publisher | : |
Total Pages | : 448 |
Release | : 1991 |
Genre | : Combinatorial analysis |
ISBN | : |
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Author | : Adalbert Kerber |
Publisher | : |
Total Pages | : 448 |
Release | : 1991 |
Genre | : Combinatorial analysis |
ISBN | : |
Author | : Adalbert Kerber |
Publisher | : Springer Science & Business Media |
Total Pages | : 488 |
Release | : 1999-08-18 |
Genre | : Mathematics |
ISBN | : 9783540659419 |
Written by one of the top experts in the fields of combinatorics and representation theory, this book distinguishes itself from the existing literature by its applications-oriented point of view. The second edition is extended, placing more emphasis on applications to the constructive theory of finite structures. Recent progress in this field, in particular in design and coding theory, is described.
Author | : Adalbert Kerber |
Publisher | : Springer Science & Business Media |
Total Pages | : 478 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662111675 |
Written by one of the top experts in the fields of combinatorics and representation theory, this book distinguishes itself from the existing literature by its applications-oriented point of view. The second edition is extended, placing more emphasis on applications to the constructive theory of finite structures. Recent progress in this field, in particular in design and coding theory, is described.
Author | : Richard P. Stanley |
Publisher | : Springer Science & Business Media |
Total Pages | : 226 |
Release | : 2013-06-17 |
Genre | : Mathematics |
ISBN | : 1461469988 |
Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.
Author | : Anton Betten |
Publisher | : Springer Science & Business Media |
Total Pages | : 358 |
Release | : 2013-11-09 |
Genre | : Mathematics |
ISBN | : 3642594484 |
Proceedings of a high-level conference on discrete mathematics, focusing on group actions in the areas of pure mathematics, applied mathematics, computer science, physics, and chemistry. A useful tool for researchers and graduate students in discrete mathematics and theoretical computer science.
Author | : Mara D. Neusel |
Publisher | : American Mathematical Soc. |
Total Pages | : 384 |
Release | : 2010-03-08 |
Genre | : Mathematics |
ISBN | : 0821849816 |
The questions that have been at the center of invariant theory since the 19th century have revolved around the following themes: finiteness, computation, and special classes of invariants. This book begins with a survey of many concrete examples chosen from these themes in the algebraic, homological, and combinatorial context. In further chapters, the authors pick one or the other of these questions as a departure point and present the known answers, open problems, and methods and tools needed to obtain these answers. Chapter 2 deals with algebraic finiteness. Chapter 3 deals with combinatorial finiteness. Chapter 4 presents Noetherian finiteness. Chapter 5 addresses homological finiteness. Chapter 6 presents special classes of invariants, which deal with modular invariant theory and its particular problems and features. Chapter 7 collects results for special classes of invariants and coinvariants such as (pseudo) reflection groups and representations of low degree. If the ground field is finite, additional problems appear and are compensated for in part by the emergence of new tools. One of these is the Steenrod algebra, which the authors introduce in Chapter 8 to solve the inverse invariant theory problem, around which the authors have organized the last three chapters. The book contains numerous examples to illustrate the theory, often of more than passing interest, and an appendix on commutative graded algebra, which provides some of the required basic background. There is an extensive reference list to provide the reader with orientation to the vast literature.
Author | : A. A. Ivanov |
Publisher | : World Scientific |
Total Pages | : 350 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 9789812564481 |
Over the past 20 years, the theory of groups in particular simplegroups, finite and algebraic has influenced a number of diverseareas of mathematics. Such areas include topics where groups have beentraditionally applied, such as algebraic combinatorics, finitegeometries, Galois theory and permutation groups, as well as severalmore recent developments.
Author | : I_A. G. Berkovich |
Publisher | : American Mathematical Soc. |
Total Pages | : 364 |
Release | : 1998-09-29 |
Genre | : Mathematics |
ISBN | : 9780821897881 |
This book places character theory and its applications to finite groups within the reach of people with a comparatively modest mathematical background. The work concentrates mostly on applications of character theory to finite groups. The main themes are degrees and kernels of irreducible characters, the class number and the number of nonlinear irreducible characters, values of irreducible characters, characterizations and generalizations of Frobenius groups, and generalizations of monomial groups. The presentation is detailed, and many proofs of known results are new.
Author | : A A Ivanov |
Publisher | : World Scientific |
Total Pages | : 348 |
Release | : 2003-03-19 |
Genre | : Mathematics |
ISBN | : 9814486426 |
Over the past 20 years, the theory of groups — in particular simple groups, finite and algebraic — has influenced a number of diverse areas of mathematics. Such areas include topics where groups have been traditionally applied, such as algebraic combinatorics, finite geometries, Galois theory and permutation groups, as well as several more recent developments. Among the latter are probabilistic and computational group theory, the theory of algebraic groups over number fields, and model theory, in each of which there has been a major recent impetus provided by simple group theory. In addition, there is still great interest in local analysis in finite groups, with substantial new input from methods of geometry and amalgams, and particular emphasis on the revision project for the classification of finite simple groups. This important book contains 20 survey articles covering many of the above developments. It should prove invaluable for those working in the theory of groups and its applications. Contents:Curtis–Phan–Tits Theory (C D Bennett et al.)Derangements in Simple and Primitive Groups (J Fulman & R Guralnick)Computing with Matrix Groups (W M Kantor & Á Seress)Bases of Primitive Permutation Groups (M W Liebeck & A Shalev)Modular Subgroup Arithmetic (T W Müller)Counting Nets in the Monster (S P Norton)Overgroups of Finite Quasiprimitive Permutation Groups (C E Praeger)Old Groups Can Learn New Tricks (L Pyber)Structure and Presentations of Lie-Type Groups (F G Timmesfeld)Computing in the Monster (R A Wilson)and other papers Readership: Graduate students, researchers and academics in algebra. Keywords:Simple Groups;Algebraic Combinatorics;Finite Geometry;Permutation Groups. Probabilistic Group
Author | : IA. G. Berkovich E. M. Zhmud' |
Publisher | : American Mathematical Soc. |
Total Pages | : 414 |
Release | : 1997-12-02 |
Genre | : |
ISBN | : 9780821897829 |
This book discusses character theory and its applications to finite groups. The work places the subject within the reach of people with a relatively modest mathematical background. The necessary background exceeds the standard algebra course with respect only to finite groups. Starting with basic notions and theorems in character theory, the authors present a variety of results on the properties of complex-valued characters and applications to finite groups. The main themes are degrees and kernels of irreducible characters, the class number and the number of nonlinear irreducible characters, values of irreducible characters, characterizations and generalizations of Frobenius groups, and generalizations and applications of monomial groups. The presentation is detailed, and many proofs of known results are new. Most of the results in the book are presented in monograph form for the first time. Numerous exercises offer additional information on the topics and help readers to understand the main concepts and results.