Oriented matroids play the role of matrices in discrete geometry, when metrical properties, such as angles or distances, are neither required nor available. Thus they are of great use in such areas as graph theory, combinatorial optimization and convex geometry. The combination of concrete applications and computation, the profusion of illustrations, many in color, and the large number of examples and exercises make this an ideal introductory text on the subject. It will also be valuable for self-study for mathematicians and computer scientists working in discrete and computational geometry.
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Editorial Reviews
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'For illustrative purposes, the book contains not only a large number of colorful pictures of oriented matroids, but also pictures of artwork, by various artists, all having oriented matroid themes; the book, itself, is perhaps a piece of art.' Zentralblatt MATH
Book Description
Oriented matroids play the role of matrices in discrete geometry, when metrical properties, such as angles or distances, are neither required nor available. Thus they are of great use in such areas as graph theory, combinatorial optimization and convex geometry. The combination of concrete applications and computation, the profusion of illustrations, and the large number of examples and exercises will make this an ideal introductory text on the subject. It will also be valuable for self-study for mathematicians and computer scientists working in discrete and computational geometry.
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Inside This Book
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First Sentence:
A matrix will be our paradigm for explaining the concept of an oriented matroid. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
hyperline sequences, big face lattice, given chirotope, oriented pseudospheres, sphere system model, matroid information, oriented pseudolines, alternating oriented matroid, chirotope axioms, corresponding chirotope, oriented matroids form, triangulated torus, uniform chirotope, matroid polytope, oriented matroid theory, topological hyperplanes, pseudoline arrangement, topological representation theorem, matroid techniques, uniform oriented matroid, star indices, map snd, incidence theorems, simplex orientations, positively oriented base Key Phrases - Capitalized Phrases (CAPs): (learn more)
Guedes de Oliveira, Las Vergnas, Felix Klein, Gutierrez Novoa, Karl Heinrich Hofmann, Snow White New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
A matrix will be our paradigm for explaining the concept of an oriented matroid. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
hyperline sequences, big face lattice, given chirotope, oriented pseudospheres, sphere system model, matroid information, oriented pseudolines, alternating oriented matroid, chirotope axioms, corresponding chirotope, oriented matroids form, triangulated torus, uniform chirotope, matroid polytope, oriented matroid theory, topological hyperplanes, pseudoline arrangement, topological representation theorem, matroid techniques, uniform oriented matroid, star indices, map snd, incidence theorems, simplex orientations, positively oriented base Key Phrases - Capitalized Phrases (CAPs): (learn more)
Guedes de Oliveira, Las Vergnas, Felix Klein, Gutierrez Novoa, Karl Heinrich Hofmann, Snow White New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
This book cites 25
books:
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- Oriented Matroids (Encyclopedia of Mathematics and its Applications) by Anders Björner on page 70, Back Matter (1), and Back Matter (2)
- Linear Programming Duality: An Introduction to Oriented Matroids (Universitext) by Achim Bachem on page 59, and Back Matter
- Lectures on Polytopes (Graduate Texts in Mathematics) by Gunter M. Ziegler on page 130, and Back Matter
- Handbook of Graph Theory (Discrete Mathematics and Its Applications) by Jonathan L. Gross in Back Matter (1), and Back Matter (2)
- Polytopes: Abstract, Convex and Computational (NATO Science Series C: (closed)) by Tibor Bisztriczky in Back Matter (1), and Back Matter (2)
See all 25 books this book cites
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