Matroids A Geometric Introduction

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Matroids A Geometric Introduction

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Author : Gary Gordon
language : en
Publisher: Cambridge University Press
Release Date : 2012-08-02

Matroids A Geometric Introduction written by Gary Gordon 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 2012-08-02 with Language Arts & Disciplines categories.

This friendly introduction helps undergraduate students understand and appreciate matroid theory and its connections to geometry.

Theory Of Matroids

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Author : Neil White
language : en
Publisher: Cambridge University Press
Release Date : 1986-04-03

Theory Of Matroids written by Neil White 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 1986-04-03 with Mathematics categories.

The theory of matroids is unique in the extent to which it connects such disparate branches of combinatorial theory and algebra as graph theory, lattice theory, design theory, combinatorial optimization, linear algebra, group theory, ring theory and field theory. Furthermore, matroid theory is alone among mathematical theories because of the number and variety of its equivalent axiom systems. Indeed, matroids are amazingly versatile and the approaches to the subject are varied and numerous. This book is a primer in the basic axioms and constructions of matroids. The contributions by various leaders in the field include chapters on axiom systems, lattices, basis exchange properties, orthogonality, graphs and networks, constructions, maps, semi-modular functions and an appendix on cryptomorphisms. The authors have concentrated on giving a lucid exposition of the individual topics; explanations of theorems are preferred to complete proofs and original work is thoroughly referenced. In addition, exercises are included for each topic.

Matroid Applications

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Author : Neil White
language : en
Publisher: Cambridge University Press
Release Date : 1992-03-05

Matroid Applications written by Neil White 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 1992-03-05 with Mathematics categories.

This volume, the third in a sequence that began with The Theory of Matroids and Combinatorial Geometries, concentrates on the applications of matroid theory to a variety of topics from engineering (rigidity and scene analysis), combinatorics (graphs, lattices, codes and designs), topology and operations research (the greedy algorithm).

Matroid Theory

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Author : D. J. A. Welsh
language : en
Publisher: Courier Corporation
Release Date : 2010-01-01

Matroid Theory written by D. J. A. Welsh and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Mathematics categories.

The theory of matroids connects disparate branches of combinatorial theory and algebra such as graph and lattice theory, combinatorial optimization, and linear algebra. This text describes standard examples and investigation results, and it uses elementary proofs to develop basic matroid properties before advancing to a more sophisticated treatment. 1976 edition.

Coxeter Matroids

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Author : Alexandre V. Borovik
language : en
Publisher: Birkhäuser
Release Date : 2003-07-11

Coxeter Matroids written by Alexandre V. Borovik and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-11 with Mathematics categories.

Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry, and "Coxeter Matroids" provides an intuitive and interdisciplinary treatment of their theory. In this text, matroids are examined in terms of symmetric and finite reflection groups; also, symplectic matroids and the more general coxeter matroids are carefully developed. The Gelfand-Serganova theorem, which allows for the geometric interpretation of matroids as convex polytopes with certain symmetry properties, is presented, and in the final chapter, matroid representations and combinatorial flag varieties are discussed. With its excellent bibliography and index and ample references to current research, this work will be useful for graduate students and research mathematicians.

Divisors And Sandpiles

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Author : Scott Corry
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-07-23

Divisors And Sandpiles written by Scott Corry and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-23 with Mathematics categories.

Divisors and Sandpiles provides an introduction to the combinatorial theory of chip-firing on finite graphs. Part 1 motivates the study of the discrete Laplacian by introducing the dollar game. The resulting theory of divisors on graphs runs in close parallel to the geometric theory of divisors on Riemann surfaces, and Part 1 culminates in a full exposition of the graph-theoretic Riemann-Roch theorem due to M. Baker and S. Norine. The text leverages the reader's understanding of the discrete story to provide a brief overview of the classical theory of Riemann surfaces. Part 2 focuses on sandpiles, which are toy models of physical systems with dynamics controlled by the discrete Laplacian of the underlying graph. The text provides a careful introduction to the sandpile group and the abelian sandpile model, leading ultimately to L. Levine's threshold density theorem for the fixed-energy sandpile Markov chain. In a precise sense, the theory of sandpiles is dual to the theory of divisors, and there are many beautiful connections between the first two parts of the book. Part 3 addresses various topics connecting the theory of chip-firing to other areas of mathematics, including the matrix-tree theorem, harmonic morphisms, parking functions, M-matrices, matroids, the Tutte polynomial, and simplicial homology. The text is suitable for advanced undergraduates and beginning graduate students.

Computational Synthetic Geometry

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Author : Jürgen Bokowski
language : en
Publisher: Springer
Release Date : 2006-11-14

Computational Synthetic Geometry written by Jürgen Bokowski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to students with graduate level background in mathematics, and will serve professional geometers and computer scientists as an introduction and motivation for further research.

Foundations Of Convex Geometry

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Author : W. A. Coppel
language : en
Publisher: Cambridge University Press
Release Date : 1998-03-05

Foundations Of Convex Geometry written by W. A. Coppel 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 1998-03-05 with Mathematics categories.

This book on the foundations of Euclidean geometry aims to present the subject from the point of view of present day mathematics, taking advantage of all the developments since the appearance of Hilbert's classic work. Here real affine space is characterised by a small number of axioms involving points and line segments making the treatment self-contained and thorough, many results being established under weaker hypotheses than usual. The treatment should be totally accessible for final year undergraduates and graduate students, and can also serve as an introduction to other areas of mathematics such as matroids and antimatroids, combinatorial convexity, the theory of polytopes, projective geometry and functional analysis.

Semidefinite Optimization And Convex Algebraic Geometry

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Author : Grigoriy Blekherman
language : en
Publisher: SIAM
Release Date : 2013-03-21

Semidefinite Optimization And Convex Algebraic Geometry written by Grigoriy Blekherman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-21 with Mathematics categories.

An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.

On The Foundations Of Combinatorial Theory Combinatorial Geometries

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Author : Henry H. Crapo
language : en
Publisher: MIT Press (MA)
Release Date : 1970

On The Foundations Of Combinatorial Theory Combinatorial Geometries written by Henry H. Crapo and has been published by MIT Press (MA) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.

A major aim of this book is to present the theory of combinatorial geometry in a form accessible to mathematicians working in disparate subjects.