Finite Geometry And Combinatorics
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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 | : 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 | : Lynn Margaret Batten |
Publisher | : Cambridge University Press |
Total Pages | : 211 |
Release | : 1997-05-28 |
Genre | : Mathematics |
ISBN | : 0521590140 |
Thoroughly revised and updated, with an entirely new chapter on blocking sets in linear spaces.
Author | : Alexander Pott |
Publisher | : Springer |
Total Pages | : 185 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540491821 |
Difference sets are of central interest in finite geometry and design theory. One of the main techniques to investigate abelian difference sets is a discrete version of the classical Fourier transform (i.e., character theory) in connection with algebraic number theory. This approach is described using only basic knowledge of algebra and algebraic number theory. It contains not only most of our present knowledge about abelian difference sets, but also gives applications of character theory to projective planes with quasiregular collineation groups. Therefore, the book is of interest both to geometers and mathematicians working on difference sets. Moreover, the Fourier transform is important in more applied branches of discrete mathematics such as coding theory and shift register sequences.
Author | : Lynn Margaret Batten |
Publisher | : Cambridge University Press |
Total Pages | : 208 |
Release | : 1997-05-28 |
Genre | : Mathematics |
ISBN | : 9780521590143 |
Combinatorics of Finite Geometries is an introductory text on the combinatorial theory of finite geometry. Assuming only a basic knowledge of set theory and analysis, it provides a thorough review of the topic and leads the student to results at the frontiers of research. This book begins with an elementary combinatorial approach to finite geometries based on finite sets of points and lines, and moves into the classical work on affine and projective planes. Later, it addresses polar spaces, partial geometries, and generalized quadrangles. The revised edition contains an entirely new chapter on blocking sets in linear spaces, which highlights some of the most important applications of blocking sets--from the initial game-theoretic setting to their very recent use in cryptography. Extensive exercises at the end of each chapter insure the usefulness of this book for senior undergraduate and beginning graduate students.
Author | : Martin W. Liebeck |
Publisher | : Cambridge University Press |
Total Pages | : 505 |
Release | : 1992-09-10 |
Genre | : Mathematics |
ISBN | : 0521406854 |
This volume contains a collection of papers on the subject of the classification of finite simple groups.
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 | : Albrecht Beutelspacher |
Publisher | : Cambridge University Press |
Total Pages | : 428 |
Release | : 1993 |
Genre | : Combinatorial analysis |
ISBN | : 9780521448505 |
Included here are articles from many of the leading practitioners in the field, including, for the first time, several distinguished Russian mathematicians. Many of the papers contain important new results, and the growing use of computer algebra packages in this area is also demonstrated.
Author | : James Hirschfeld |
Publisher | : Springer |
Total Pages | : 422 |
Release | : 2016-02-03 |
Genre | : Mathematics |
ISBN | : 1447167902 |
This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume). This revised edition includes much updating and new material. It is a mostly self-contained study of classical varieties over a finite field, related incidence structures and particular point sets in finite n-dimensional projective spaces. General Galois Geometries is suitable for PhD students and researchers in combinatorics and geometry. The separate chapters can be used for courses at postgraduate level.
Author | : Albrecht Beutelspacher |
Publisher | : Cambridge University Press |
Total Pages | : 70 |
Release | : 1993 |
Genre | : Combinatorial analysis |
ISBN | : 9780521448505 |
Included here are articles from many of the leading practitioners in the field, including, for the first time, several distinguished Russian mathematicians. Many of the papers contain important new results, and the growing use of computer algebra packages in this area is also demonstrated.