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LCP Degree Theory and Oriented Matroids
SIAM Journal on Matrix Analysis and Applications, 1994Summary: It is shown that the degree of a square-oriented matroid \(\mathcal M\) can be defined in terms of the number of solutions to the oriented matroid complementarity problem defined by a point extension of \(\mathcal M\), and that this definition is independent of the point extension. If \(\mathcal M\) is represented by a matrix \([I, -M]\), then
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Applications of Matroid Theory
1983It will be shown that looking at a problem from the viewpoint of matroids enables us to understand the essence of the problem as well as its relations to other problems, clearly, preventing us from probable confusion into which we might have been involved without matroids, and that mathematical techniques developed in matroid theory are powerful for ...
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Recursion Theory on Matroids II
1983Publisher Summary This chapter discusses the recursion theory on matroids II. The recursion theory is developed on vector spaces, on algebraically closed fields, and on a common generalization of vectors spaces and algebraically closed fields. This is the theory of abstract transitive dependence relations or matroids.
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Basic concepts in matroid theory
1989Since the introduction of 2-isomorphism we saw several examples, both in the theory and its applications, where not all the properties of a graph play a role; in most cases only subgraphs with or without circuits need to be distinguished. Similarly, sign conventions or the underlying field for the matrices of the graphs were not important; we did not ...
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