Author : Paul-Hermann Zieschang
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 47,83 MB
Release : 2005-10-20
Category : Mathematics
ISBN : 9783540261360
This book is a concept-oriented treatment of the structure theory of association schemes. The generalization of Sylow’s group theoretic theorems to scheme theory arises as a consequence of arithmetical considerations about quotient schemes. The theory of Coxeter schemes (equivalent to the theory of buildings) emerges naturally and yields a purely algebraic proof of Tits’ main theorem on buildings of spherical type.
Author : R. A. Bailey
Publisher : Cambridge University Press
Page : 410 pages
File Size : 35,24 MB
Release : 2004-02-26
Category : Mathematics
ISBN : 9781139449939
Association schemes are of interest to both mathematicians and statisticians and this book was written with both audiences in mind. For statisticians, it shows how to construct designs for experiments in blocks, how to compare such designs, and how to analyse data from them. The reader is only assumed to know very basic abstract algebra. For pure mathematicians, it tells why association schemes are important and develops the theory to the level of advanced research. This book arose from a course successfully taught by the author and as such the material is thoroughly class-tested. There are a great number of examples and exercises that will increase the book's appeal to both graduate students and their instructors. It is ideal for those coming either from pure mathematics or statistics backgrounds who wish to develop their understanding of association schemes.
Author : Eiichi Bannai
Publisher : Walter de Gruyter GmbH & Co KG
Page : 303 pages
File Size : 35,10 MB
Release : 2021-02-22
Category : Mathematics
ISBN : 3110627736
This series is devoted to the publication of high-level monographs which cover the whole spectrum of current discrete mathematics and its applications in various fields. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of discrete mathematics. Contributions which are on the borderline of discrete mathematics and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.
Author : Alexander Barg
Publisher : American Mathematical Soc.
Page : 317 pages
File Size : 35,49 MB
Release : 2001
Category : Computers
ISBN : 0821820745
This volume presents papers related to the DIMACS workshop, "Codes and Association Schemes". The articles are devoted to the following topics: applications of association schemes and of the polynomial method to properties of codes, structural results for codes, structural results for association schemes, and properties of orthogonal polynomials and their applications in combinatorics. Papers on coding theory are related to classical topics, such as perfect codes, bounds on codes, codes and combinatorial arrays, weight enumerators, and spherical designs. Papers on orthogonal polynomials provide new results on zeros and symptotic properties of standard families of polynomials encountered in coding theory. The theme of association schemes is represented by new classification results and new classes of schemes related to posets. This volume collects up-to-date applications of the theory of association schemes to coding and presents new properties of both polynomial and general association schemes. It offers a solid representation of results in problems in areas of current interest.
Author : David Eisenbud
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 40,20 MB
Release : 2006-04-06
Category : Mathematics
ISBN : 0387226397
Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
Author : K. T. Arasu
Publisher : Walter de Gruyter
Page : 333 pages
File Size : 44,74 MB
Release : 2008-08-22
Category : Mathematics
ISBN : 3110198118
Following an initiative of the late Hans Zassenhaus in 1965, the Departments of Mathematics at The Ohio State University and Denison University organize conferences in combinatorics, group theory, and ring theory. Between May 18-21, 2000, the 25th conference of this series was held. Usually, there are twenty to thirty invited 20-minute talks in each of the three main areas. However, at the 2000 meeting, the combinatorics part of the conference was extended, to honor the 65th birthday of Professor Dijen Ray-Chaudhuri. This volulme is the proceedings of this extension. Most of the papers are in coding theory and design theory, reflecting the major interest of Professor Ray-Chaudhuri, but there are articles on association schemes, algebraic graph theory, combinatorial geometry, and network flows as well. There are four surveys and seventeen research articles, and all of these went through a thorough refereeing process. The volume is primarily recommended for researchers and graduate students interested in new developments in coding theory and design theory.
Author : Raj Chandra Bose
Publisher :
Page : 62 pages
File Size : 45,82 MB
Release : 1958
Category : Algebras, Linear
ISBN :
Author : Neil deMause
Publisher : U of Nebraska Press
Page : 479 pages
File Size : 17,41 MB
Release : 2015-03
Category : Architecture
ISBN : 0803285485
Author : David Bourqui
Publisher : World Scientific
Page : 312 pages
File Size : 38,44 MB
Release : 2020-03-05
Category : Mathematics
ISBN : 1786347210
This title introduces the theory of arc schemes in algebraic geometry and singularity theory, with special emphasis on recent developments around the Nash problem for surfaces. The main challenges are to understand the global and local structure of arc schemes, and how they relate to the nature of the singularities on the variety. Since the arc scheme is an infinite dimensional object, new tools need to be developed to give a precise meaning to the notion of a singular point of the arc scheme.Other related topics are also explored, including motivic integration and dual intersection complexes of resolutions of singularities. Written by leading international experts, it offers a broad overview of different applications of arc schemes in algebraic geometry, singularity theory and representation theory.
Author : Eiichi Bannai
Publisher : Walter de Gruyter GmbH & Co KG
Page : 444 pages
File Size : 32,12 MB
Release : 2021-02-22
Category : Mathematics
ISBN : 3110630257
Algebraic combinatorics is the study of combinatorial objects as an extension of the study of finite permutation groups, or, in other words, group theory without groups. In the spirit of Delsarte's theory, this book studies combinatorial objects such as graphs, codes, designs, etc. in the general framework of association schemes, providing a comprehensive overview of the theory as well as pointing out to extensions.
