Handbook Of Finite Translation Planes
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Handbook Of Finite Translation Planes
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Author : Norman Johnson
language : en
Publisher: CRC Press
Release Date : 2007-02-15
Handbook Of Finite Translation Planes written by Norman Johnson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-15 with Mathematics categories.
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
General Galois Geometries
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Author : James Hirschfeld
language : en
Publisher: Springer
Release Date : 2016-02-03
General Galois Geometries written by James Hirschfeld and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-03 with Mathematics categories.
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.
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.
Geometry Of Derivation With Applications
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Author : Norman L. Johnson
language : en
Publisher: CRC Press
Release Date : 2023-06-06
Geometry Of Derivation With Applications written by Norman L. Johnson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-06 with Mathematics categories.
Geometry of Derivation with Applications is the fifth work in a longstanding series of books on combinatorial geometry (Subplane Covered Nets, Foundations of Translation Planes, Handbook of Finite Translation Planes, and Combinatorics of Spreads and Parallelisms). Like its predecessors, this book will primarily deal with connections to the theory of derivable nets and translation planes in both the finite and infinite cases. Translation planes over non-commutative skewfields have not traditionally had a significant representation in incidence geometry, and derivable nets over skewfields have only been marginally understood. Both are deeply examined in this volume, while ideas of non-commutative algebra are also described in detail, with all the necessary background given a geometric treatment. The book builds upon over twenty years of work concerning combinatorial geometry, charted across four previous books and is suitable as a reference text for graduate students and researchers. It contains a variety of new ideas and generalizations of established work in finite affine geometry and is replete with examples and applications.
Combinatorics Of Spreads And Parallelisms
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Author : Norman Johnson
language : en
Publisher: CRC Press
Release Date : 2010-06-03
Combinatorics Of Spreads And Parallelisms written by Norman Johnson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-03 with Mathematics categories.
Combinatorics of Spreads and Parallelisms covers all known finite and infinite parallelisms as well as the planes comprising them. It also presents a complete analysis of general spreads and partitions of vector spaces that provide groups enabling the construction of subgeometry partitions of projective spaces.The book describes general partitions
Handbook Of Incidence Geometry
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Author : Francis Buekenhout
language : en
Publisher: North-Holland
Release Date : 1995
Handbook Of Incidence Geometry written by Francis Buekenhout and has been published by North-Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
Hardbound. This Handbook deals with the foundations of incidence geometry, in relationship with division rings, rings, algebras, lattices, groups, topology, graphs, logic and its autonomous development from various viewpoints. Projective and affine geometry are covered in various ways. Major classes of rank 2 geometries such as generalized polygons and partial geometries are surveyed extensively.More than half of the book is devoted to buildings at various levels of generality, including a detailed and original introduction to the subject, a broad study of characterizations in terms of points and lines, applications to algebraic groups, extensions to topological geometry, a survey of results on diagram geometries and nearby generalizations such as matroids.
Bent Functions
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Author : Sihem Mesnager
language : en
Publisher: Springer
Release Date : 2016-08-09
Bent Functions written by Sihem Mesnager and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-09 with Computers categories.
This book gives a detailed survey of the main results on bent functions over finite fields, presents a systematic overview of their generalizations, variations and applications, considers open problems in classification and systematization of bent functions, and discusses proofs of several results. This book uniquely provides a necessary comprehensive coverage of bent functions.It serves as a useful reference for researchers in discrete mathematics, coding and cryptography. Students and professors in mathematics and computer science will also find the content valuable, especially those interested in mathematical foundations of cryptography. It can be used as a supplementary text for university courses on discrete mathematics, Boolean functions, or cryptography, and is appropriate for both basic classes for under-graduate students and advanced courses for specialists in cryptography and mathematics.
Handbook Of Combinatorics
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Author : R.L. Graham
language : en
Publisher: Elsevier
Release Date : 1995-12-11
Handbook Of Combinatorics written by R.L. Graham and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-11 with Computers categories.
Handbook of Combinatorics
Handbook Of Combinatorics Volume 1
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Author : Bozzano G Luisa
language : en
Publisher: Elsevier
Release Date : 1995-12-11
Handbook Of Combinatorics Volume 1 written by Bozzano G Luisa and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-11 with Computers categories.
Handbook of Combinatorics, Volume 1 focuses on basic methods, paradigms, results, issues, and trends across the broad spectrum of combinatorics. The selection first elaborates on the basic graph theory, connectivity and network flows, and matchings and extensions. Discussions focus on stable sets and claw free graphs, nonbipartite matching, multicommodity flows and disjoint paths, minimum cost circulations and flows, special proof techniques for paths and circuits, and Hamilton paths and circuits in digraphs. The manuscript then examines coloring, stable sets, and perfect graphs and embeddings and minors. The book takes a look at random graphs, hypergraphs, partially ordered sets, and matroids. Topics include geometric lattices, structural properties, linear extensions and correlation, dimension and posets of bounded degree, hypergraphs and set systems, stability, transversals, and matchings, and phase transition. The manuscript also reviews the combinatorial number theory, point lattices, convex polytopes and related complexes, and extremal problems in combinatorial geometry. The selection is a valuable reference for researchers interested in combinatorics.
Lattice Basis Reduction
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Author : Murray R. Bremner
language : en
Publisher: CRC Press
Release Date : 2011-08-12
Lattice Basis Reduction written by Murray R. Bremner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-12 with Computers categories.
First developed in the early 1980s by Lenstra, Lenstra, and Lovász, the LLL algorithm was originally used to provide a polynomial-time algorithm for factoring polynomials with rational coefficients. It very quickly became an essential tool in integer linear programming problems and was later adapted for use in cryptanalysis. This book provides an introduction to the theory and applications of lattice basis reduction and the LLL algorithm. With numerous examples and suggested exercises, the text discusses various applications of lattice basis reduction to cryptography, number theory, polynomial factorization, and matrix canonical forms.