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| Author | : Earl Sidney Kramer |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 332 |
| Release | : 1990 |
| Genre | : Mathematics |
| ISBN | : 0821851187 |
The proceedings of an AMS special session on finite geometries and combinatorial designs. Topics range over finite geometry, combinatorial designs, their automorphism groups and related structures.
| Author | : J. W. P. Hirschfeld |
| Publisher | : Cambridge University Press |
| Total Pages | : 269 |
| Release | : 1997-08-14 |
| Genre | : Mathematics |
| ISBN | : 052159538X |
This volume examines state of the art research in finite geometries and designs.
| Author | : Steven T. Dougherty |
| Publisher | : Springer Nature |
| Total Pages | : 374 |
| Release | : 2020-10-30 |
| Genre | : Mathematics |
| ISBN | : 3030563952 |
This undergraduate textbook is suitable for introductory classes in combinatorics and related topics. The book covers a wide range of both pure and applied combinatorics, beginning with the very basics of enumeration and then going on to Latin squares, graphs and designs. The latter topic is closely related to finite geometry, which is developed in parallel. Applications to probability theory, algebra, coding theory, cryptology and combinatorial game theory comprise the later chapters. Throughout the book, examples and exercises illustrate the material, and the interrelations between the various topics is emphasized. Readers looking to take first steps toward the study of combinatorics, finite geometry, design theory, coding theory, or cryptology will find this book valuable. Essentially self-contained, there are very few prerequisites aside from some mathematical maturity, and the little algebra required is covered in the text. The book is also a valuable resource for anyone interested in discrete mathematics as it ties together a wide variety of topics.
| Author | : Kathleen Quinn |
| Publisher | : Taylor & Francis |
| Total Pages | : 160 |
| Release | : 2023-02-06 |
| Genre | : Mathematics |
| ISBN | : 1351459740 |
The fruit of a conference that gathered seven very active researchers in the field, Combinatorial Design and their Applications presents a wide but representative range of topics on the non-geometrical aspects of design theory. By concentrating on a few important areas, the authors succeed in providing greater detail in these areas in a more complete and accessible form. Through their contributions to this collection, they help fill a gap in the available combinatorics literature.The papers included in this volume cover recent developments in areas of current interest, such as difference sets, cryptography, and optimal linear codes. Researchers in combinatorics and other areas of pure mathematics, along with researchers in statistics and computer design will find in-depth, up-to-date discussions of design theory and the application of the theory to statistical design, codes, and cryptography.
| Author | : Simeon Ball |
| Publisher | : Cambridge University Press |
| Total Pages | : 299 |
| Release | : 2015-06-26 |
| Genre | : Mathematics |
| ISBN | : 1316301044 |
The projective and polar geometries that arise from a vector space over a finite field are particularly useful in the construction of combinatorial objects, such as latin squares, designs, codes and graphs. This book provides an introduction to these geometries and their many applications to other areas of combinatorics. Coverage includes a detailed treatment of the forbidden subgraph problem from a geometrical point of view, and a chapter on maximum distance separable codes, which includes a proof that such codes over prime fields are short. The author also provides more than 100 exercises (complete with detailed solutions), which show the diversity of applications of finite fields and their geometries. Finite Geometry and Combinatorial Applications is ideal for anyone, from a third-year undergraduate to a researcher, who wishes to familiarise themselves with and gain an appreciation of finite geometry.
| Author | : Earl Sidney Kramer |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 334 |
| Release | : 1990-11-20 |
| Genre | : Mathematics |
| ISBN | : 9780821854440 |
More than eighty participants from all over the world attended an AMS Special Session on Finite Geometries and Combinatorial Designs held in Lincoln, Nebraska, in the fall of 1987. This volume contains the proceedings of that Special Session, in addition to several invited papers. Employing state-of-the-art combinatorial and geometric methods, the papers show significant advances in this area. Topics range over finite geometry, combinatorial designs, their automorphism groups, and related structures. Requiring graduate-level background, this book is intended primarily for researchers in finite geometries and combinatorial designs. However, the interested nonspecialist will find that the book provides an excellent overview of current activity in these areas.
| Author | : W.D. Wallis |
| Publisher | : CRC Press |
| Total Pages | : 324 |
| Release | : 2016-04-19 |
| Genre | : Computers |
| ISBN | : 1584888393 |
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
| Author | : Steven T. Dougherty |
| Publisher | : Springer |
| Total Pages | : 369 |
| Release | : 2020-10-31 |
| Genre | : Mathematics |
| ISBN | : 9783030563943 |
This undergraduate textbook is suitable for introductory classes in combinatorics and related topics. The book covers a wide range of both pure and applied combinatorics, beginning with the very basics of enumeration and then going on to Latin squares, graphs and designs. The latter topic is closely related to finite geometry, which is developed in parallel. Applications to probability theory, algebra, coding theory, cryptology and combinatorial game theory comprise the later chapters. Throughout the book, examples and exercises illustrate the material, and the interrelations between the various topics is emphasized. Readers looking to take first steps toward the study of combinatorics, finite geometry, design theory, coding theory, or cryptology will find this book valuable. Essentially self-contained, there are very few prerequisites aside from some mathematical maturity, and the little algebra required is covered in the text. The book is also a valuable resource for anyone interested in discrete mathematics as it ties together a wide variety of topics.
| Author | : Yury J. Ionin |
| Publisher | : Cambridge University Press |
| Total Pages | : 8 |
| Release | : 2006-05-25 |
| Genre | : Mathematics |
| ISBN | : 1139449664 |
The aim of this book is to provide a unified exposition of the theory of symmetric designs with emphasis on recent developments. The authors cover the combinatorial aspects of the theory giving particular attention to the construction of symmetric designs and related objects. The last five chapters of the book are devoted to balanced generalized weighing matrices, decomposable symmetric designs, subdesigns of symmetric designs, non-embeddable quasi-residual designs, and Ryser designs. Most results in these chapters have never previously appeared in book form. The book concludes with a comprehensive bibliography of over 400 entries. Researchers in all areas of combinatorial designs, including coding theory and finite geometries, will find much of interest here. Detailed proofs and a large number of exercises make this book suitable as a text for an advanced course in combinatorial designs.
| Author | : P. J. Cameron |
| Publisher | : Cambridge University Press |
| Total Pages | : 381 |
| Release | : 1981-04-16 |
| Genre | : Mathematics |
| ISBN | : 0521283787 |
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.
