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The oriented matroid of a finite configuration of points extracts relative position and orientation information from the configuration. An oriented matroid can be described ...

Roughly speaking, a matroid is a finite set together with a generalization of a concept from linear algebra that satisfies a natural set of properties for that concept. For ...

Suppose that G is a pseudograph, E is the edge set of G, and C is the family of edge sets of graph cycles of G. Then C obeys the axioms for the circuits of a matroid, and ...

An oriented knot is an oriented link of one component, or equivalently, it is a knot which has been given an orientation. Given an oriented knot K, reversing the orientation ...

An oriented graph is a directed graph having no symmetric pair of directed edges. A complete oriented graph is called a tournament. The numbers of oriented graphs on n=1, 2, ...

An oriented link is a link for which each connected component has been given an orientation. As oriented links are equivalent, if there is an orientation preserving ...

A lattice L is said to be oriented if there exists a rule which assigns a specified direction to any edge connecting arbitrary lattice points x_i,x_j in L. In that way, an ...

A d-dimensional discrete percolation model on a regular point lattice L=L^d is said to be oriented if L is an oriented lattice. One common such model takes place on the ...

Perhaps the most commonly-studied oriented point lattice is the so-called north-east lattice which orients each edge of L in the direction of increasing coordinate-value. ...

The word configuration is sometimes used to describe a finite collection of points p=(p_1,...,p_n), p_i in R^d, where R^d is a Euclidean space. The term "configuration" also ...