Overview of the Matroids:-ExampleMatroids Subpackage
Calling Sequence
Parameters
Description
Examples
References
Fano()
Hesse()
MacLane()
NCubeMatroid(n)
NonFano()
NonPappus()
Pappus()
TicTacToe()
UniformMatroid(r,n)
Vamos()
r
-
integer
n
There are several standard constructions of matroids in the literature. We list some below.
The Fano matroid: A matroid which is not representable over the real numbers, but is representable over the field with two elements.
The Hesse matroid: The matroid underlying a Hesse configuration of nine points.
The MacLane matroid: Obtained by deleting any element from the ground set of the Hesse matroid. This matroid is non-orientable.
The NCube matroid: The matroid underlying the vertices of an n dimensional cube.
The NonFano matroid: The matroid obtained by removing one non-basis from the Fano matroid.
The NonPappus matroid: The matroid obtained by removing one non-basis from the Pappus matroid.
The Pappus matroid: The matroid on nine points realizing the collinearities of Pappus' theorem.
The Tic-Tac-Toe matroid: A matroid on nine points whose dual is non-algebraic. It is unknown if the tic-tac-toe matroid is algebraic.
The uniform matroid: A matroid where every r subset of n elements is a basis.
The Vamos matroid: The smallest matroid which is not representable over any field.
withMatroids:
withExampleMatroids:
Create a matroid from the ExampleMatroids gallery.
M≔UniformMatroid3,7
M≔thⅇ unⅈform matroⅈⅆ of rank 3 on 7 ⅇlⅇmⅇnts
evalbnumelemsBasesM=binomial7,3
true
AreIsomorphicDeletionHesse,1,MacLane
James G. Oxley. Matroid Theory (Oxford Graduate Texts in Mathematics). New York: Oxford University Press. 2006.
See Also
Matroids[Matroid]
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