Matroid
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In combinatorics, a branch of mathematics, a matroid or independence structure is a structure that captures the essence of a notion of "independence" that generalizes linear independence in vector spaces. There are many equivalent ways to define a matroid, and many concepts within matroid theory have a variety of equivalent formulations. Depending on the sophistication of the concept, it may be nontrivial to show that the different formulations are equivalent, a phenomenon sometimes called cryptomorphism. Significant definitions of matroid include those in terms of independent sets, bases, cir...
In combinatorics, a branch of mathematics, a matroid or independence structure is a structure that captures the essence of a notion of "independence" that generalizes linear independence in vector spaces. There are many equivalent ways to define a matroid, and many concepts within matroid theory have a variety of equivalent formulations. Depending on the sophistication of the concept, it may be nontrivial to show that the different formulations are equivalent, a phenomenon sometimes called cryptomorphism. Significant definitions of matroid include those in terms of independent sets, bases, circuits, closed sets or flats, closure operators, and rank functions. Matroid theory borrows extensively from the terminology of linear algebra and graph theory, largely because it is the abstraction of various notions of central importance in these fields.
