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Finite Geometry and Combinatorial Applications

2015-06-26 Mathematics
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Release : 2015-06-26
Genre : Mathematics
Kind : eBook
Book Rating : 044/5 ( reviews)

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Book Synopsis Finite Geometry and Combinatorial Applications by : Simeon Ball

Download or read book Finite Geometry and Combinatorial Applications written by Simeon Ball. This book was released on 2015-06-26. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Combinatorics and Finite Geometry

2020-10-30 Mathematics
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Release : 2020-10-30
Genre : Mathematics
Kind : eBook
Book Rating : 952/5 ( reviews)

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Book Synopsis Combinatorics and Finite Geometry by : Steven T. Dougherty

Download or read book Combinatorics and Finite Geometry written by Steven T. Dougherty. This book was released on 2020-10-30. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Finite Geometries

2014-05-12 Mathematics
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Release : 2014-05-12
Genre : Mathematics
Kind : eBook
Book Rating : 14X/5 ( reviews)

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Book Synopsis Introduction to Finite Geometries by : F. Kárteszi

Download or read book Introduction to Finite Geometries written by F. Kárteszi. This book was released on 2014-05-12. Available in PDF, EPUB and Kindle. Book excerpt: North-Holland Texts in Advanced Mathematics: Introduction to Finite Geometries focuses on the advancements in finite geometries, including mapping and combinatorics. The manuscript first offers information on the basic concepts on finite geometries and Galois geometries. Discussions focus on linear mapping of a given quadrangle onto another given quadrangle; point configurations of order 2 on a Galois plane of even order; canonical equation of curves of the second order on the Galois planes of even order; and set of collineations mapping a Galois plane onto itself. The text then ponders on geometrical configurations and nets, as well as pentagon theorem and the Desarguesian configuration, two pentagons inscribed into each other, and the concept of geometrical nets. The publication takes a look at combinatorial applications of finite geometries and combinatorics and finite geometries. Topics include generalizations of the Petersen graph, combinatorial extremal problem, and theorem of closure of the hyperbolic space. The book is a valuable source of data for readers interested in finite geometries.

Finite Geometry and Combinatorial Applications

2015-07-02 Mathematics
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Release : 2015-07-02
Genre : Mathematics
Kind : eBook
Book Rating : 997/5 ( reviews)

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Book Synopsis Finite Geometry and Combinatorial Applications by : Simeon Ball

Download or read book Finite Geometry and Combinatorial Applications written by Simeon Ball. This book was released on 2015-07-02. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.

Finite Geometries

2019-07-26 Mathematics
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Release : 2019-07-26
Genre : Mathematics
Kind : eBook
Book Rating : 389/5 ( reviews)

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Book Synopsis Finite Geometries by : Gyorgy Kiss

Download or read book Finite Geometries written by Gyorgy Kiss. This book was released on 2019-07-26. Available in PDF, EPUB and Kindle. Book excerpt: Finite Geometries stands out from recent textbooks about the subject of finite geometries by having a broader scope. The authors thoroughly explain how the subject of finite geometries is a central part of discrete mathematics. The text is suitable for undergraduate and graduate courses. Additionally, it can be used as reference material on recent works. The authors examine how finite geometries’ applicable nature led to solutions of open problems in different fields, such as design theory, cryptography and extremal combinatorics. Other areas covered include proof techniques using polynomials in case of Desarguesian planes, and applications in extremal combinatorics, plus, recent material and developments. Features: Includes exercise sets for possible use in a graduate course Discusses applications to graph theory and extremal combinatorics Covers coding theory and cryptography Translated and revised text from the Hungarian published version

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