Combinatorics And Finite Geometry

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Combinatorics and Finite Geometry

Steven T. Dougherty
Combinatorics and Finite Geometry Book PDF

Author : Steven T. Dougherty
Publisher : Springer Nature
Page : 374 pages
File Size : 48,6 Mb
Release : 2020-10-30
Category : Mathematics
ISBN : 9783030563950

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Combinatorics and Finite Geometry by Steven T. Dougherty Pdf

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.

Combinatorics and Finite Geometry

Steven T. Dougherty
Combinatorics and Finite Geometry Book PDF

Author : Steven T. Dougherty
Publisher : Springer
Page : 369 pages
File Size : 51,8 Mb
Release : 2020-10-31
Category : Mathematics
ISBN : 3030563944

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Combinatorics and Finite Geometry by Steven T. Dougherty Pdf

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.

Combinatorics of Finite Geometries

Lynn Margaret Batten
Combinatorics of Finite Geometries Book PDF

Author : Lynn Margaret Batten
Publisher : Cambridge University Press
Page : 211 pages
File Size : 44,6 Mb
Release : 1997-05-28
Category : Mathematics
ISBN : 9780521590143

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Combinatorics of Finite Geometries by Lynn Margaret Batten Pdf

Thoroughly revised and updated, with an entirely new chapter on blocking sets in linear spaces.

Finite Geometries

Gyorgy Kiss,Tamas Szonyi
Finite Geometries Book PDF

Author : Gyorgy Kiss,Tamas Szonyi
Publisher : CRC Press
Page : 274 pages
File Size : 49,9 Mb
Release : 2019-07-26
Category : Mathematics
ISBN : 9781351646383

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Finite Geometries by Gyorgy Kiss,Tamas Szonyi Pdf

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

Finite Geometries and Combinatorics

Albrecht Beutelspacher,F. de Clerck
Finite Geometries and Combinatorics Book PDF

Author : Albrecht Beutelspacher,F. de Clerck
Publisher : Cambridge University Press
Page : 428 pages
File Size : 40,9 Mb
Release : 1993-10-21
Category : Mathematics
ISBN : 0521448506

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Finite Geometries and Combinatorics by Albrecht Beutelspacher,F. de Clerck Pdf

This is a collection of thirty-five articles, covering topics such as finite projective spaces, generalized polygons, strongly regular graphs, diagram geometries, and polar spaces. Contained 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.

Combinatorics of Finite Geometries

L. M. Batten
Combinatorics of Finite Geometries Book PDF

Author : L. M. Batten
Publisher : Cambridge University Press
Page : 183 pages
File Size : 42,9 Mb
Release : 1986-03-31
Category : Mathematics
ISBN : 0521267641

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Combinatorics of Finite Geometries by L. M. Batten Pdf

This textbook is intended as an introduction to the combinatorial theory of finite geometry for undergraduate students of mathematics. Although only a basic knowledge of set theory and analysis is assumed, the student is soon led Op results at the frontiers of research. Professor Batten begins with a discussion of near-linear spaces before proceeding to treat linear, projective and affine spaces. This half of the book in itself would be suitable for use as a text for a course in synthethic geometry. The remainder of the book is devoted to the relatively new areas of polar spaces, generalized quadrangles and partial geometries. These subjects are currently the focus of much research in combinatorial geometry.

Finite Geometry and Character Theory

Alexander Pott
Finite Geometry and Character Theory Book PDF

Author : Alexander Pott
Publisher : Springer
Page : 185 pages
File Size : 54,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540491828

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Finite Geometry and Character Theory by Alexander Pott Pdf

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.

Finite Geometry and Combinatorial Applications

Simeon Ball
Finite Geometry and Combinatorial Applications Book PDF

Author : Simeon Ball
Publisher : Cambridge University Press
Page : 299 pages
File Size : 51,9 Mb
Release : 2015-07-02
Category : Mathematics
ISBN : 9781107107991

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Finite Geometry and Combinatorial Applications by Simeon Ball Pdf

A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.

Groups, Combinatorics and Geometry

Martin W. Liebeck
Groups Combinatorics and Geometry Book PDF

Author : Martin W. Liebeck
Publisher : Cambridge University Press
Page : 505 pages
File Size : 41,8 Mb
Release : 1992-09-10
Category : Mathematics
ISBN : 9780521406857

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Groups, Combinatorics and Geometry by Martin W. Liebeck Pdf

This volume contains a collection of papers on the subject of the classification of finite simple groups.

Finite Geometries and Combinatorics

Albrecht Beutelspacher,F. de Clerck
Finite Geometries and Combinatorics Book PDF

Author : Albrecht Beutelspacher,F. de Clerck
Publisher : Cambridge University Press
Page : 70 pages
File Size : 49,9 Mb
Release : 1993-10-21
Category : Mathematics
ISBN : 0521448506

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Finite Geometries and Combinatorics by Albrecht Beutelspacher,F. de Clerck Pdf

This is a collection of thirty-five articles, covering topics such as finite projective spaces, generalized polygons, strongly regular graphs, diagram geometries, and polar spaces. Contained 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.

Introduction to Finite Geometries

F. Kárteszi
Introduction to Finite Geometries Book PDF

Author : F. Kárteszi
Publisher : Elsevier
Page : 280 pages
File Size : 43,7 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483278148

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Introduction to Finite Geometries by F. Kárteszi Pdf

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.

An Introduction to Finite Projective Planes

Abraham Adrian Albert,Reuben Sandler
An Introduction to Finite Projective Planes Book PDF

Author : Abraham Adrian Albert,Reuben Sandler
Publisher : Courier Corporation
Page : 116 pages
File Size : 43,8 Mb
Release : 2015-02-18
Category : Mathematics
ISBN : 9780486789941

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An Introduction to Finite Projective Planes by Abraham Adrian Albert,Reuben Sandler Pdf

Text for both beginning and advanced undergraduate and graduate students covers finite planes, field planes, coordinates in an arbitrary plane, central collineations and the little Desargues' property, the fundamental theorem, and non-Desarguesian planes. 1968 edition.

Finite Geometries and Combinatorial Designs

Earl Sidney Kramer
Finite Geometries and Combinatorial Designs Book PDF

Author : Earl Sidney Kramer
Publisher : American Mathematical Soc.
Page : 312 pages
File Size : 43,6 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821851180

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Finite Geometries and Combinatorial Designs by Earl Sidney Kramer Pdf

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.

Discrete Geometry and Algebraic Combinatorics

Alexander Barg,Oleg R. Musin
Discrete Geometry and Algebraic Combinatorics Book PDF

Author : Alexander Barg,Oleg R. Musin
Publisher : American Mathematical Society
Page : 202 pages
File Size : 49,5 Mb
Release : 2014-08-28
Category : Mathematics
ISBN : 9781470409050

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Discrete Geometry and Algebraic Combinatorics by Alexander Barg,Oleg R. Musin Pdf

This volume contains the proceedings of the AMS Special Session on Discrete Geometry and Algebraic Combinatorics held on January 11, 2013, in San Diego, California. The collection of articles in this volume is devoted to packings of metric spaces and related questions, and contains new results as well as surveys of some areas of discrete geometry. This volume consists of papers on combinatorics of transportation polytopes, including results on the diameter of graphs of such polytopes; the generalized Steiner problem and related topics of the minimal fillings theory; a survey of distance graphs and graphs of diameters, and a group of papers on applications of algebraic combinatorics to packings of metric spaces including sphere packings and topics in coding theory. In particular, this volume presents a new approach to duality in sphere packing based on the Poisson summation formula, applications of semidefinite programming to spherical codes and equiangular lines, new results in list decoding of a family of algebraic codes, and constructions of bent and semi-bent functions.

Advanced Combinatorics

Louis Comtet
Advanced Combinatorics Book PDF

Author : Louis Comtet
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401021968

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Advanced Combinatorics by Louis Comtet Pdf

Notwithstanding its title, the reader will not find in this book a systematic account of this huge subject. Certain classical aspects have been passed by, and the true title ought to be "Various questions of elementary combina torial analysis". For instance, we only touch upon the subject of graphs and configurations, but there exists a very extensive and good literature on this subject. For this we refer the reader to the bibliography at the end of the volume. The true beginnings of combinatorial analysis (also called combina tory analysis) coincide with the beginnings of probability theory in the 17th century. For about two centuries it vanished as an autonomous sub ject. But the advance of statistics, with an ever-increasing demand for configurations as well as the advent and development of computers, have, beyond doubt, contributed to reinstating this subject after such a long period of negligence. For a long time the aim of combinatorial analysis was to count the different ways of arranging objects under given circumstances. Hence, many of the traditional problems of analysis or geometry which are con cerned at a certain moment with finite structures, have a combinatorial character. Today, combinatorial analysis is also relevant to problems of existence, estimation and structuration, like all other parts of mathema tics, but exclusively forjinite sets.