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Questions related to the field of Combinatorics called Matroid Theory. Relevant topics include matroids in Combinatorial Optimization, Lattice Theory, Algebraic Geometry, Polyhedral Theory, Rigidity, and Algorithms. For questions about Oriented Matroids, the oriented-matroids tag may be used.
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matroids axioms and independence system
A finite matroid $M$ is a pair $(E,I)$ where $E$ is a finite set and $I$ is a family of independent set with the following properties:
1) There is at least an independent system
2) Every subset of a …