Abstract
The viewpoint of the subject of matroids, and related areas of lattice theory, has always been, in one way or another, abstraction of algebraic dependence or, equivalently, abstraction of the incidence relations in geometric representations of algebra. Often one of the main derived facts is that all bases have the same cardinality. (See Van der Waerden, Section 33.)
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Edmonds, J. (2003). Submodular Functions, Matroids, and Certain Polyhedra. In: Jünger, M., Reinelt, G., Rinaldi, G. (eds) Combinatorial Optimization — Eureka, You Shrink!. Lecture Notes in Computer Science, vol 2570. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36478-1_2
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DOI: https://doi.org/10.1007/3-540-36478-1_2
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