Some Topics In Combinatorial Design Theory And Algebraic Graph Theory
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Some Topics In Combinatorial Design Theory And Algebraic Graph Theory
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Author : Nick C. Fiala
language : en
Publisher:
Release Date : 2002
Some Topics In Combinatorial Design Theory And Algebraic Graph Theory written by Nick C. Fiala and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
Combinatorial Design Theory
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Author : C.J. Colbourn
language : en
Publisher: Elsevier
Release Date : 2011-09-22
Combinatorial Design Theory written by C.J. Colbourn and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-22 with Mathematics categories.
Combinatorial design theory is a vibrant area of combinatorics, connecting graph theory, number theory, geometry, and algebra with applications in experimental design, coding theory, and numerous applications in computer science. This volume is a collection of forty-one state-of-the-art research articles spanning all of combinatorial design theory. The articles develop new methods for the construction and analysis of designs and related combinatorial configurations; both new theoretical methods, and new computational tools and results, are presented. In particular, they extend the current state of knowledge on Steiner systems, Latin squares, one-factorizations, block designs, graph designs, packings and coverings, and develop recursive and direct constructions. The contributions form an overview of the current diversity of themes in design theory for those peripherally interested, while researchers in the field will find it to be a major collection of research advances. The volume is dedicated to Alex Rosa, who has played a major role in fostering and developing combinatorial design theory.
Hypergraphs And Designs
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Author : Mario Gionfriddo
language : en
Publisher: Nova Science Publishers
Release Date : 2015
Hypergraphs And Designs written by Mario Gionfriddo and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Hypergraphs categories.
Combinatorial designs represent an important area of contemporary discrete mathematics closely related to such fields as finite geometries, regular graphs and multigraphs, factorisations of graphs, linear algebra, number theory, finite fields, group and quasigroup theory, Latin squares, and matroids. It has a history of more than 150 years when it started as a collection of unrelated problems. Nowadays the field is a well-developed theory with deep mathematical results and a wide range of applications in coding theory, cryptography, computer science, and other areas. In the most general setting, a combinatorial design consists of a ground set of elements and a collection of subsets of these elements satisfying some specific restrictions; the latter are often expressed in the language of graphs. On the other side, hypergraph theory is a relatively new field which started in early 60s of the last century as a generalization of graph theory. A hypergraph consists of a ground set of elements and a collection of subsets of these elements without any specific restrictions. In this sense the concept of hypergraph is more general than the concept of combinatorial design. While it started as a generalization of graph theory, hypergraph theory soon became a separate subject because many new properties have been discovered that miss or degenerate in graphs. Compared to graph theory, the language of hypergraphs not only allows us to formulate and solve more general problems, it also helps us to understand and solve several graph theory problems by simplifying and unifying many previously unrelated concepts. The main feature of this book is applying the hypergraph approach to the theory of combinatorial designs. An alternative title of it could be "Combinatorial designs as hypergraphs". There is no analogue to this book on the market. Its primary audience is researchers and graduate students taking courses in design theory, combinatorial geometry, finite geometry, discrete mathematics, graph theory, combinatorics, cryptography, information and coding theory, and similar areas. The aim of this book is to show the connection and mutual benefit between hypergraph theory and design theory. It does not intend to give a survey of all important results or methods in any of these subjects.
Algorithms In Combinatorial Design Theory
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Author : C.J. Colbourn
language : en
Publisher: Elsevier
Release Date : 1985-01-01
Algorithms In Combinatorial Design Theory written by C.J. Colbourn and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-01 with Mathematics categories.
The scope of the volume includes all algorithmic and computational aspects of research on combinatorial designs. Algorithmic aspects include generation, isomorphism and analysis techniques - both heuristic methods used in practice, and the computational complexity of these operations. The scope within design theory includes all aspects of block designs, Latin squares and their variants, pairwise balanced designs and projective planes and related geometries.
Combinatorial Methods With Computer Applications
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Author : Jonathan L. Gross
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Combinatorial Methods With Computer Applications written by Jonathan L. Gross and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Computers categories.
Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinat
Applications Of Group Theory To Combinatorics
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Author : Jack Koolen
language : en
Publisher: CRC Press
Release Date : 2008-07-02
Applications Of Group Theory To Combinatorics written by Jack Koolen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-02 with Mathematics categories.
Applications of Group Theory to Combinatorics contains 11 survey papers from international experts in combinatorics, group theory and combinatorial topology. The contributions cover topics from quite a diverse spectrum, such as design theory, Belyi functions, group theory, transitive graphs, regular maps, and Hurwitz problems, and present the state
Topics In Graph Theory
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Author : Jonathan L Gross
language : en
Publisher: CRC Press
Release Date : 2023-05-24
Topics In Graph Theory written by Jonathan L Gross and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-24 with Mathematics categories.
The interplay continues to grow between graph theory and a wide variety of models and applications in mathematics, computer science, operations research, and the natural and social sciences. Topics in Graph Theory is geared toward the more mathematically mature student. The first three chapters provide the basic definitions and theorems of graph theory and the remaining chapters introduce a variety of topics and directions for research. These topics draw on numerous areas of theoretical and applied mathematics, including combinatorics, probability, linear algebra, group theory, topology, operations research, and computer science. This makes the book appropriate for a first course at the graduate level or as a second course at the undergraduate level. The authors build upon material previously published in Graph Theory and Its Applications, Third Edition, by the same authors. That text covers material for both an undergraduate and graduate course, while this book builds on and expands the graduate-level material. Features Extensive exercises and applications. Flexibility: appropriate for either a first course at the graduate level or an advanced course at the undergraduate level. Opens avenues to a variety of research areas in graph theory. Emphasis on topological and algebraic graph theory.
Algebraic Design Theory
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Author : Warwick De Launey
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Algebraic Design Theory written by Warwick De Launey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Combinatorial design theory is a source of simply stated, concrete, yet difficult discrete problems, with the Hadamard conjecture being a prime example. It has become clear that many of these problems are essentially algebraic in nature. This book provides a unified vision of the algebraic themes which have developed so far in design theory. These include the applications in design theory of matrix algebra, the automorphism group and its regular subgroups, the composition of smaller designs to make larger designs, and the connection between designs with regular group actions and solutions to group ring equations. Everything is explained at an elementary level in terms of orthogonality sets and pairwise combinatorial designs--new and simple combinatorial notions which cover many of the commonly studied designs. Particular attention is paid to how the main themes apply in the important new context of cocyclic development. Indeed, this book contains a comprehensive account of cocyclic Hadamard matrices. The book was written to inspire researchers, ranging from the expert to the beginning student, in algebra or design theory, to investigate the fundamental algebraic problems posed by combinatorial design theory.
Introduction To Combinatorial Designs
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Author : W.D. Wallis
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Introduction To Combinatorial Designs written by W.D. Wallis and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Computers categories.
Combinatorial theory is one of the fastest growing areas of modern mathematics. Focusing on a major part of this subject, Introduction to Combinatorial Designs, Second Edition provides a solid foundation in the classical areas of design theory as well as in more contemporary designs based on applications in a variety of fields. After an o
Handbook Of Graph Theory Combinatorial Optimization And Algorithms
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Author : Krishnaiyan "KT" Thulasiraman
language : en
Publisher: CRC Press
Release Date : 2016-01-05
Handbook Of Graph Theory Combinatorial Optimization And Algorithms written by Krishnaiyan "KT" Thulasiraman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-05 with Computers categories.
The fusion between graph theory and combinatorial optimization has led to theoretically profound and practically useful algorithms, yet there is no book that currently covers both areas together. Handbook of Graph Theory, Combinatorial Optimization, and Algorithms is the first to present a unified, comprehensive treatment of both graph theory and c