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:
“Both of us felt more anxiety about the South—about the colored people especially—than about anything else sinister in the result. My hope of a sound currency will somehow be realized; civil service reform will be delayed; but the great injury is in the South. There the Amendments will be nullified, disorder will continue, prosperity to both whites and colored people will be pushed off for years.”
—Rutherford Birchard Hayes (1822–1893)