Matroid Applications: Encyclopedia of Mathematics and its Applications 40

Matroid Applications (Encyclopedia of Mathematics and its Applications Book 40)

by Ann Angel

4.7 out of 5

Language	:	English
File size	:	21723 KB
Print length	:	376 pages
Hardcover	:	72 pages
Item Weight	:	9 ounces
Dimensions	:	5.98 x 0.25 x 9.02 inches
Screen Reader	:	Supported

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Matroid Applications, part of the Encyclopedia of Mathematics and its Applications series, is a valuable resource for researchers and practitioners in the field of matroid theory. This comprehensive volume provides in-depth coverage of the applications of matroid theory in a wide range of areas, including combinatorics, computer science, operations research, and geometry.

Table of Contents

• Matroids in Combinatorics
• Matroids in Computer Science
• Matroids in Operations Research
• Matroids in Geometry
• Applications in Other Areas
• References

Matroid theory is a branch of mathematics that studies a class of combinatorial structures called matroids. Matroids have a wide range of applications in other areas of mathematics, including combinatorics, computer science, operations research, and geometry.

The basic definition of a matroid is as follows: A matroid is a pair (M, I),where M is a finite set and I is a collection of subsets of M that satisfy the following axioms:

1. The empty set is in I.
2. If X is in I and Y is a subset of X, then Y is in I.
3. If X and Y are in I, then there exists a Z in I such that X ∪ Y ⊆ Z.

Matroids can be used to represent a wide variety of combinatorial structures, including graphs, hypergraphs, and matrices. They can also be used to solve a variety of combinatorial problems, such as finding the maximum weight independent set in a graph or the minimum cost spanning tree in a network.

Matroids in Combinatorics

Matroids have a wide range of applications in combinatorics. They can be used to solve a variety of combinatorial problems, such as finding the maximum weight independent set in a graph or the minimum cost spanning tree in a network.

One of the most important applications of matroids in combinatorics is in the area of graph theory. Matroids can be used to represent graphs, and the properties of matroids can be used to study the properties of graphs. For example, the Tutte polynomial of a graph can be expressed in terms of the matroid associated with the graph.

Matroids in Computer Science

Matroids have a wide range of applications in computer science. They can be used to solve a variety of problems in computer science, such as finding the maximum weight matching in a graph or the minimum cost flow in a network.

One of the most important applications of matroids in computer science is in the area of optimization. Matroids can be used to model a variety of optimization problems, and the properties of matroids can be used to develop efficient algorithms for solving these problems.

Matroids in Operations Research

Matroids have a wide range of applications in operations research. They can be used to solve a variety of problems in operations research, such as finding the maximum weight independent set in a graph or the minimum cost spanning tree in a network.

One of the most important applications of matroids in operations research is in the area of scheduling. Matroids can be used to model a variety of scheduling problems, and the properties of matroids can be used to develop efficient algorithms for solving these problems.

Matroids in Geometry

Matroids have a wide range of applications in geometry. They can be used to solve a variety of problems in geometry, such as finding the maximum weight independent set in a graph or the minimum cost spanning tree in a network.

One of the most important applications of matroids in geometry is in the area of polytope theory. Matroids can be used to represent polytopes, and the properties of matroids can be used to study the properties of polytopes.

Applications in Other Areas

Matroids have a wide range of applications in other areas, such as physics, economics, and biology. They can be used to solve a variety of problems in these areas, such as finding the maximum weight independent set in a graph or the minimum cost spanning tree in a network.

One of the most important applications of matroids in other areas is in the area of physics. Matroids can be used to model a variety of physical systems, and the properties of matroids can be used to study the properties of these systems.

References

[1] J. G. Oxley, Matroid Theory, Oxford University Press, 1992.

[2] A. Björner, M. Las Vergnas, B. Sturmfels, N. White, and G. Ziegler, Oriented Matroids, Cambridge University Press, 1999.

[3] J. E. Bonin and J. G. Oxley, T

Matroid Applications (Encyclopedia of Mathematics and its Applications Book 40)

by Ann Angel

4.7 out of 5

Language	:	English
File size	:	21723 KB
Print length	:	376 pages
Hardcover	:	72 pages
Item Weight	:	9 ounces
Dimensions	:	5.98 x 0.25 x 9.02 inches
Screen Reader	:	Supported

FREE