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Unitals in Projective Planes

Unitals in Projective Planes PDF Author: Susan Barwick
Publisher: Springer Science & Business Media
ISBN: 038776366X
Category : Mathematics
Languages : en
Pages : 197

Book Description
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

Unitals in Projective Planes PDF Author: Susan Barwick
Publisher: Springer Science & Business Media
ISBN: 038776366X
Category : Mathematics
Languages : en
Pages : 197

Book Description
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

Compact Projective Planes PDF Author: Helmut Salzmann
Publisher: Walter de Gruyter
ISBN: 3110876833
Category : Mathematics
Languages : en
Pages : 705

Book Description
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics 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 wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, 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 and Z. Janko, Groups of Prime Power Order, Volume 6 (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, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Handbook of Finite Translation Planes

Handbook of Finite Translation Planes PDF Author: Norman Johnson
Publisher: CRC Press
ISBN: 1420011146
Category : Mathematics
Languages : en
Pages : 884

Book Description
The Handbook of Finite Translation Planes provides a comprehensive listing of all translation planes derived from a fundamental construction technique, an explanation of the classes of translation planes using both descriptions and construction methods, and thorough sketches of the major relevant theorems. From the methods of Andre to coordi

Handbook of Combinatorial Designs

Handbook of Combinatorial Designs PDF Author: Charles J. Colbourn
Publisher: CRC Press
ISBN: 1420010549
Category : Computers
Languages : en
Pages : 1011

Book Description
Continuing in the bestselling, informative tradition of the first edition, the Handbook of Combinatorial Designs, Second Edition remains the only resource to contain all of the most important results and tables in the field of combinatorial design. This handbook covers the constructions, properties, and applications of designs as well as existence

Geometries and Groups

Geometries and Groups PDF Author: M. Aigner
Publisher: Springer
ISBN: 3540386394
Category : Mathematics
Languages : en
Pages : 262

Book Description
Dedicated to Professor Dr. Hanfried Lenz on the Occasion of his 65th Birthday

Topics on Steiner Systems

Topics on Steiner Systems PDF Author:
Publisher: Elsevier
ISBN: 0080867707
Category : Mathematics
Languages : en
Pages : 361

Book Description
Topics on Steiner Systems

Handbook of Finite Fields

Handbook of Finite Fields PDF Author: Gary L. Mullen
Publisher: CRC Press
ISBN: 1439873828
Category : Computers
Languages : en
Pages : 1048

Book Description
Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and

Designs and Their Codes

Designs and Their Codes PDF Author: E. F. Assmus
Publisher: Cambridge University Press
ISBN: 9780521458399
Category : Mathematics
Languages : en
Pages : 366

Book Description
A self-contained account suited for a wide audience describing coding theory, combinatorial designs and their relations.

Design Theory: Volume 1

Design Theory: Volume 1 PDF Author: Thomas Beth
Publisher: Cambridge University Press
ISBN: 9780521444323
Category : Mathematics
Languages : en
Pages : 730

Book Description
This is the first volume of the second edition of the standard text on design theory.

A Geometrical Picture Book

A Geometrical Picture Book PDF Author: Burkard Polster
Publisher: Springer Science & Business Media
ISBN: 1441985263
Category : Mathematics
Languages : en
Pages : 302

Book Description
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.