Download or read book Handbook of Combinatorics written by R.L. Graham and published by Elsevier. This book was released on 1995-12-11 with total page 2404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Combinatorics

Download or read book Investigations in Algebraic Theory of Combinatorial Objects written by I.A. Faradzev and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: X 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.

Download or read book Permutation Groups and Cartesian Decompositions written by Cheryl E. Praeger and published by Cambridge University Press. This book was released on 2018-05-03 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Permutation groups, their fundamental theory and applications are discussed in this introductory book. It focuses on those groups that are most useful for studying symmetric structures such as graphs, codes and designs. Modern treatments of the O'Nan–Scott theory are presented not only for primitive permutation groups but also for the larger families of quasiprimitive and innately transitive groups, including several classes of infinite permutation groups. Their precision is sharpened by the introduction of a cartesian decomposition concept. This facilitates reduction arguments for primitive groups analogous to those, using orbits and partitions, that reduce problems about general permutation groups to primitive groups. The results are particularly powerful for finite groups, where the finite simple group classification is invoked. Applications are given in algebra and combinatorics to group actions that preserve cartesian product structures. Students and researchers with an interest in mathematical symmetry will find the book enjoyable and useful.

Download or read book Distance Regular Graphs written by Andries E. Brouwer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since the discovery of the five platonic solids in ancient times, the study of symmetry and regularity has been one of the most fascinating aspects of mathematics. Quite often the arithmetical regularity properties of an object imply its uniqueness and the existence of many symmetries. This interplay between regularity and symmetry properties of graphs is the theme of this book. Starting from very elementary regularity properties, the concept of a distance-regular graph arises naturally as a common setting for regular graphs which are extremal in one sense or another. Several other important regular combinatorial structures are then shown to be equivalent to special families of distance-regular graphs. Other subjects of more general interest, such as regularity and extremal properties in graphs, association schemes, representations of graphs in euclidean space, groups and geometries of Lie type, groups acting on graphs, and codes are covered independently. Many new results and proofs and more than 750 references increase the encyclopaedic value of this book.

Download or read book Mathematical Reviews written by and published by . This book was released on 2002 with total page 1092 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Imprimitive Distance transitive Graphs written by Monther Rashed Furaidan and published by . This book was released on 2004 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometry of Matrices written by Zhexian Wan and published by World Scientific. This book was released on 1996 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph is a state-of-art survey of the geometry of matrices whose study was initiated by L K Hua in the forties. The geometry of rectangular matrices, of alternate matrices, of symmetric matrices, and of hermitian matrices over a division ring or a field are studied in detail. The author's recent results on geometry of symmetric matrices and of hermitian matrices are included. A chapter on linear algebra over a division ring and one on affine and projective geometry over a division ring are also included. The book is clearly written so that graduate students and third or fourth year undergraduate students in mathematics can read it without difficulty.

Download or read book Topics in Algebraic Graph Theory written by Lowell W. Beineke and published by Cambridge University Press. This book was released on 2004-10-04 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). These areas have links with other areas of mathematics, such as logic and harmonic analysis, and are increasingly being used in such areas as computer networks where symmetry is an important feature. Other books cover portions of this material, but this book is unusual in covering both of these aspects and there are no other books with such a wide scope. Peter J. Cameron, internationally recognized for his substantial contributions to the area, served as academic consultant for this volume, and the result is ten expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory, linear algebra and group theory. Each chapter concludes with an extensive list of references.

Download or read book Combinatorial Mathematics IX written by E. J. Billington and published by Springer. This book was released on 2006-11-15 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Finite Geometries and Designs written by P. J. Cameron and published by Cambridge University Press. This book was released on 1981-04-16 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1981 collection of 33 research papers follows from a conference on the interwoven themes of finite Desarguesian spaces and Steiner systems, amongst other topics.

Download or read book Groups and Graphs Designs and Dynamics written by R. A. Bailey and published by Cambridge University Press. This book was released on 2024-05-30 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.

Download or read book Groups and Computation written by Larry Finkelstein and published by American Mathematical Soc.. This book was released on 1993-01-01 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers presented at the Workshop on Groups and Computation, held in October, 1991. The workshop explored interactions among four areas: symbolic algebra and computer algebra, theoretical computer science, group theory, and applications of group computation. The relationships between implementation and complexity form a recurrent theme, though the papers also discuss such topics as parallel algorithms for groups, computation in associative algebras, asymptotic behavior of permutation groups, the study of finite groups using infinite reflection groups, combinatorial searching, computing with representations, and Cayley graphs as models for interconnection networks.

Download or read book Graph Symmetry written by Gena Hahn and published by Springer Science & Business Media. This book was released on 1997-06-30 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of such graphs. A number of symposia and congresses (such as the bi-annual IWIN, starting in 1991) bear witness to the interest of the computer science community in this subject. On the mathematical side, and independently of any interest in applications, progress in group theory has made it possible to make a realistic attempt at a complete description of vertex-transitive graphs. The classification of the finite simple groups has played an important role in this respect.

Download or read book Strongly Regular Graphs written by Andries E. Brouwer and published by Cambridge University Press. This book was released on 2022-01-13 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Strongly regular graphs lie at the intersection of statistical design, group theory, finite geometry, information and coding theory, and extremal combinatorics. This monograph collects all the major known results together for the first time in book form, creating an invaluable text that researchers in algebraic combinatorics and related areas will refer to for years to come. The book covers the theory of strongly regular graphs, polar graphs, rank 3 graphs associated to buildings and Fischer groups, cyclotomic graphs, two-weight codes and graphs related to combinatorial configurations such as Latin squares, quasi-symmetric designs and spherical designs. It gives the complete classification of rank 3 graphs, including some new constructions. More than 100 graphs are treated individually. Some unified and streamlined proofs are featured, along with original material including a new approach to the (affine) half spin graphs of rank 5 hyperbolic polar spaces.

Download or read book Surveys in Combinatorics 2021 written by Konrad K. Dabrowski and published by Cambridge University Press. This book was released on 2021-06-24 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: These nine articles provide up-to-date surveys of topics of contemporary interest in combinatorics.

Download or read book Groups and Geometries written by Lino Di Martino and published by Birkhäuser. This book was released on 2013-12-01 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of finite characteristic, 3. buildings, and the geometry of projective and polar spaces, and 4. geometries of sporadic simple groups. We are grateful to the authors for their efforts in providing us with manuscripts in LaTeX. Barbara Priwitzer and Thomas Hintermann, Mathematics Editors of Birkhauser, have been very helpful and supportive throughout the preparation of this volume.

Download or read book Report PM R written by and published by . This book was released on 1984 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: