Codes of Designs and Graphs from Finite Simple Groups
Author: Bernardo Gabriel Rodrigues
Publisher:
Published: 2002
Total Pages:
ISBN-13:
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Author: Bernardo Gabriel Rodrigues
Publisher:
Published: 2002
Total Pages:
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DOWNLOAD EBOOKAuthor: Robert Fitzgerald Morse
Publisher: American Mathematical Soc.
Published: 2014-02-13
Total Pages: 202
ISBN-13: 0821894358
DOWNLOAD EBOOKThis volume contains the proceedings of the International Conference on Group Theory, Combinatorics and Computing held from October 3-8, 2012, in Boca Raton, Florida. The papers cover a number of areas in group theory and combinatorics. Topics include finite simple groups, groups acting on structured sets, varieties of algebras, classification of groups generated by 3-state automata over a 2-letter alphabet, new methods for construction of codes and designs, groups with constraints on the derived subgroups of its subgroups, graphs related to conjugacy classes in groups, and lexicographical configurations. Application of computer algebra programs is incorporated in several of the papers. This volume includes expository articles on finite coverings of loops, semigroups and groups, and on the application of algebraic structures in the theory of communications. This volume is a valuable resource for researchers and graduate students working in group theory and combinatorics. The articles provide excellent examples of the interplay between the two areas.
Author: Manjul Bhargava
Publisher: American Mathematical Soc.
Published: 2017-07-24
Total Pages: 242
ISBN-13: 1470436787
DOWNLOAD EBOOKClassification of Finite Simple Groups, one of the most monumental accomplishments of modern mathematics, was announced in 1983 with the proof completed in 2004. Since then, it has opened up a new and powerful strategy to approach and resolve many previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy crucially utilizes various information about finite simple groups, part of which is catalogued in the Atlas of Finite Groups (John H. Conway et al.), and in An Atlas of Brauer Characters (Christoph Jansen et al.). It is impossible to overestimate the roles of the Atlases and the related computer algebra systems in the everyday life of researchers in many areas of contemporary mathematics. The main objective of the conference was to discuss numerous applications of the Atlases and to explore recent developments and future directions of research, with focus on the interaction between computation and theory and applications to number theory and algebraic geometry. The papers in this volume are based on talks given at the conference. They present a comprehensive survey on current research in all of these fields.
Author: Dean Crnković
Publisher: IOS Press
Published: 2011
Total Pages: 460
ISBN-13: 1607506629
DOWNLOAD EBOOK"Published in cooperation with NATO Emerging Security Challenges Division"--T.p.
Author: R.L. Graham
Publisher: Elsevier
Published: 1995-12-11
Total Pages: 1283
ISBN-13: 044488002X
DOWNLOAD EBOOKAuthor: I.A. Faradzev
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 513
ISBN-13: 9401719721
DOWNLOAD EBOOKX Köchendorffer, L.A. Kalu:lnin and their students in the 50s and 60s. Nowadays the most deeply developed is the theory of binary invariant relations and their combinatorial approximations. These combinatorial approximations arose repeatedly during this century under various names (Hecke algebras, centralizer rings, association schemes, coherent configurations, cellular rings, etc.-see the first paper of the collection for details) andin various branches of mathematics, both pure and applied. One of these approximations, the theory of cellular rings (cellular algebras), was developed at the end of the 60s by B. Yu. Weisfeiler and A.A. Leman in the course of the first serious attempt to study the complexity of the graph isomorphism problem, one of the central problems in the modern theory of combinatorial algorithms. At roughly the same time G.M. Adelson-Velskir, V.L. Arlazarov, I.A. Faradtev and their colleagues had developed a rather efficient tool for the constructive enumeration of combinatorial objects based on the branch and bound method. By means of this tool a number of "sports-like" results were obtained. Some of these results are still unsurpassed.
Author: E. F. Assmus
Publisher: Cambridge University Press
Published: 1994-01-06
Total Pages: 366
ISBN-13: 9780521458399
DOWNLOAD EBOOKA self-contained account suited for a wide audience describing coding theory, combinatorial designs and their relations.
Author: Thomas Beth
Publisher: Cambridge University Press
Published: 1999-11-18
Total Pages: 730
ISBN-13: 9780521444323
DOWNLOAD EBOOKThis is the first volume of the second edition of the standard text on design theory.
Author: Cheryl E. Praeger
Publisher: Cambridge University Press
Published: 1996-12-05
Total Pages: 157
ISBN-13: 0521567378
DOWNLOAD EBOOKThis book presents a complete classification of the transitive permutation representations of rank at most five of the sporadic simple groups and their automorphism groups, together with a comprehensive study of the vertex-transitive graphs associated with these representations. Included is a list of all vertex-transitive, distance-regular graphs on which a sporadic almost simple group acts with rank at most five. In this list are some new, interesting distance-regular graphs of diameter two, which are not distance-transitive. For most of the representations a presentation of the sporadic group is given, with words in the given generators which generate a point stabiliser: this gives readers sufficient information to reconstruct and study the representations and graphs. Practical computational techniques appropriate for analysing finite vertex-transitive graphs are described carefully, making the book an excellent starting point for learning about groups and the graphs on which they act.
Author: W.A. Coppel
Publisher: Springer Science & Business Media
Published: 2009-10-03
Total Pages: 620
ISBN-13: 0387894861
DOWNLOAD EBOOKNumber Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study.