Matroid

In combinatorics, a branch of mathematics, a matroid is a structure that captures the essence of a notion of "independence" that generalizes linear independence in vector spaces. (The pronunciation of the first syllable is as in mate, may, or matrix.)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.
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