Unitals In Projective Planes
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Unitals In Projective Planes
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Author : Susan Barwick
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-03
Unitals In Projective Planes written by Susan Barwick and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-03 with Mathematics categories.
This book is a monograph on unitals embedded in ?nite projective planes. Unitals are an interesting structure found in square order projective planes, and numerous research articles constructing and discussing these structures have appeared in print. More importantly, there still are many open pr- lems, and this remains a fruitful area for Ph.D. dissertations. Unitals play an important role in ?nite geometry as well as in related areas of mathematics. For example, unitals play a parallel role to Baer s- planes when considering extreme values for the size of a blocking set in a square order projective plane (see Section 2.3). Moreover, unitals meet the upper bound for the number of absolute points of any polarity in a square order projective plane (see Section 1.5). From an applications point of view, the linear codes arising from unitals have excellent technical properties (see 2 Section 6.4). The automorphism group of the classical unitalH =H(2,q ) is 2-transitive on the points ofH, and so unitals are of interest in group theory. In the ?eld of algebraic geometry over ?nite ?elds,H is a maximal curve that contains the largest number of F -rational points with respect to its genus, 2 q as established by the Hasse-Weil bound.
Unitals In Projective Planes
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Author : Susan Barwick
language : en
Publisher: Springer
Release Date : 2008-11-01
Unitals In Projective Planes written by Susan Barwick and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-01 with Mathematics categories.
This book is a monograph on unitals embedded in ?nite projective planes. Unitals are an interesting structure found in square order projective planes, and numerous research articles constructing and discussing these structures have appeared in print. More importantly, there still are many open pr- lems, and this remains a fruitful area for Ph.D. dissertations. Unitals play an important role in ?nite geometry as well as in related areas of mathematics. For example, unitals play a parallel role to Baer s- planes when considering extreme values for the size of a blocking set in a square order projective plane (see Section 2.3). Moreover, unitals meet the upper bound for the number of absolute points of any polarity in a square order projective plane (see Section 1.5). From an applications point of view, the linear codes arising from unitals have excellent technical properties (see 2 Section 6.4). The automorphism group of the classical unitalH =H(2,q ) is 2-transitive on the points ofH, and so unitals are of interest in group theory. In the ?eld of algebraic geometry over ?nite ?elds,H is a maximal curve that contains the largest number of F -rational points with respect to its genus, 2 q as established by the Hasse-Weil bound.
Compact Projective Planes
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Author : H. Salzmann
language : en
Publisher: Walter de Gruyter
Release Date : 1995
Compact Projective Planes written by H. Salzmann and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Cear , Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
A Geometrical Picture Book
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Author : Burkard Polster
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-17
A Geometrical Picture Book written by Burkard Polster and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-17 with Mathematics categories.
How do you convey to your students, colleagues and friends some of the beauty of the kind of mathematics you are obsessed with? If you are a mathematician interested in finite or topological geometry and combinatorial designs, you could start by showing them some of the (400+) pictures in the "picture book". Pictures are what this book is all about; original pictures of everybody's favorite geometries such as configurations, projective planes and spaces, circle planes, generalized polygons, mathematical biplanes and other designs which capture much of the beauty, construction principles, particularities, substructures and interconnections of these geometries. The level of the text is suitable for advanced undergraduates and graduate students. Even if you are a mathematician who just wants some interesting reading you will enjoy the author's very original and comprehensive guided tour of small finite geometries and geometries on surfaces This guided tour includes lots of sterograms of the spatial models, games and puzzles and instructions on how to construct your own pictures and build some of the spatial models yourself.
Strongly Regular Graphs
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Author : Andries E. Brouwer
language : en
Publisher:
Release Date : 2022-01-13
Strongly Regular Graphs written by Andries E. Brouwer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-13 with Language Arts & Disciplines categories.
This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.
Finite Geometries
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Author : Gyorgy Kiss
language : en
Publisher: CRC Press
Release Date : 2019-07-26
Finite Geometries written by Gyorgy Kiss and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-26 with Mathematics categories.
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
Generalized Polygons
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Author : Hendrik,van Maldeghem
language : en
Publisher: Birkhäuser
Release Date : 2013-11-09
Generalized Polygons written by Hendrik,van Maldeghem and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-09 with Mathematics categories.
This book is intended to be an introduction to the fascinating theory ofgeneralized polygons for both the graduate student and the specialized researcher in the field. It gathers together a lot of basic properties (some of which are usually referred to in research papers as belonging to folklore) and very recent and sometimes deep results. I have chosen a fairly strict geometrical approach, which requires some knowledge of basic projective geometry. Yet, it enables one to prove some typically group-theoretical results such as the determination of the automorphism groups of certain Moufang polygons. As such, some basic group-theoretical knowledge is required of the reader. The notion of a generalized polygon is a relatively recent one. But it is one of the most important concepts in incidence geometry. Generalized polygons are the building bricks of Tits buildings. They are the prototypes and precursors of more general geometries such as partial geometries, partial quadrangles, semi-partial ge ometries, near polygons, Moore geometries, etc. The main examples of generalized polygons are the natural geometries associated with groups of Lie type of relative rank 2. This is where group theory comes in and we come to the historical raison d'etre of generalized polygons. In 1959 Jacques Tits discovered the simple groups of type 3D by classifying the 4 trialities with at least one absolute point of a D -geometry. The method was 4 predominantly geometric, and so not surprisingly the corresponding geometries (the twisted triality hexagons) came into play. Generalized hexagons were born.
Unitals Embedded In Finite Projective Planes
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Author : Kenneth L. Wantz
language : en
Publisher:
Release Date : 1995
Unitals Embedded In Finite Projective Planes written by Kenneth L. Wantz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
Designs And Their Codes
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Author : E. F. Assmus
language : en
Publisher: Cambridge University Press
Release Date : 1994-01-06
Designs And Their Codes written by E. F. Assmus and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-06 with Mathematics categories.
A self-contained account suited for a wide audience describing coding theory, combinatorial designs and their relations.
Finite Geometry And Combinatorial Applications
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Author : Simeon Ball
language : en
Publisher: Cambridge University Press
Release Date : 2015-07-02
Finite Geometry And Combinatorial Applications written by Simeon Ball and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-02 with Mathematics categories.
A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.