A Characterization of the Orientations of Ternary Matroids

A Modular Triple Characterization of Lifting Signatures, Weak Orientations, Orientations, and Ternary Signatures of Matroids

For a matroid M , Dowling and Kelly show how to use a special class of its circuits, which we call balanced circuits, to construct a lift of M. In the case where M comes from a graph, Zaslavsky defines balanced circuits in terms of gains, which are group elements that label the edges of the graph. I will use gains to define the balanced circuits of an arbitrary matroid and show that the lift co...

CHARACTERIZATION OF L-FUZZIFYING MATROIDS BY L-FUZZIFYING CLOSURE OPERATORS

An L-fuzzifying matroid is a pair (E, I), where I is a map from2E to L satisfying three axioms. In this paper, the notion of closure operatorsin matroid theory is generalized to an L-fuzzy setting and called L-fuzzifyingclosure operators. It is proved that there exists a one-to-one correspondencebetween L-fuzzifying matroids and their L-fuzzifying closure operators.

A characterization of triple semigroup of ternary functions and Demorgan triple semigroup of ternary functions

On the decomposition of ternary matroids

Matroids were introduced by Whitney in 1935 to try to capture abstractly the essence of dependence. Matroids generalize linear dependence over vector spaces, and they also abstract the properties of graphs, in the former case they are called Vector Matroids, in the latter they are called Graphic Matroids [3]. The operation of Matroid Union was introduced by Nash-Williams in 1966. A matroid is i...

On the Excluded Minors for the Matroids That Are Either Binary or Ternary

The classes of binary and ternary matroids are both relatively well understood as is their intersection, the class of regular matroids. This paper considers the union M of the classes of binary and ternary matroids. M is a minor-closed class and the focus of the paper is on determining its set of excluded minors. It is conjectured here that this set of excluded minors unique matroids that are o...