Colored matroid
Encyclopedia
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).
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a colored matroid is a matroid
Matroid
In combinatorics, a branch of mathematics, a matroid or independence structure is a structure that captures the essence of a notion of "independence" that generalizes linear independence in vector spaces....
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
Tutte polynomial
The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a polynomial in two variables which plays an important role in graph theory, a branch of mathematics and theoretical computer science...
, which generalizes the Tutte polynomial of a signed graph of Kauffman (1989).