Non-interval greedoids and the transposition property
The authors study the common combinatorial structure of various recursive deletion procedures. Some of these (like shelling away endpoints of a tree, or vertices of the convex hull of a point set in \(R^ n\), or minimal elements of a poset) lead to greedoids with the interval property. However, some others, the so called non-interval greedoids, are also related to important procedures (like Gaussian elimination, blossom trees, series-parallel decomposition, ear-decomposition, retracting and dismantling). The present paper studies such greedoids and various exchange properties. One of them leads to the definition of transposition greedoids.
scientific article; zbMATH DE number 3963848
scientific article