In mathematics, a colored matroid is a matroid whose elements are labeled from a set of colors, which can be any set that suits the purpose, for instance the set of the first n positive integers, or the sign set {+, −}.
The interest in colored matroids is through their invariants, especially the colored Tutte polynomial, which generalizes the Tutte polynomial of a signed graph of Kauffman (1989).
There has also been study of optimization problems on matroids where the objective function of the optimization depends on the set of colors chosen as part of a matroid basis.
Famous quotes containing the word colored:
“If a liberal policy towards the late Rebels is adopted, the ultra Republicans are opposed to it; if the colored people are honored, the extremists of the other wing cry out against it. I suspect I am right in both cases.”
—Rutherford Birchard Hayes (1822–1893)