Dimension | Matroid theory

Matroid rank

In the mathematical theory of matroids, the rank of a matroid is the maximum size of an independent set in the matroid. The rank of a subset S of elements of the matroid is, similarly, the maximum size of an independent subset of S, and the rank function of the matroid maps sets of elements to their ranks. The rank function is one of the fundamental concepts of matroid theory via which matroids may be axiomatized. Matroid rank functions form an important subclass of the submodular set functions. The rank functions of matroids defined from certain other types of mathematical object such as undirected graphs, matrices, and field extensions are important within the study of those objects. (Wikipedia).

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Maximin share | Monotonic function | Vector space | Linear algebra | Submodular set function | Transcendence degree | Uniform matroid | Maximum cardinality matching | Fair item allocation | Graphic matroid | Linear independence | Partition matroid | Free matroid | Matroid | Envy-free item allocation | Field extension | Graph theory | Concave function | Dimension (vector space) | Circuit rank | Integer | Algebraic independence | Abstract algebra | Matrix (mathematics) | Leximin order | Matroid oracle | Rank (linear algebra) | Parameterized complexity