Antimatroids, betweenness, convexity

Abstract

Two classical examples of antimatroids arise from double shellings of partially ordered sets and from simplicial shellings of triangulated graphs. The corresponding convex geometries have Carathéodory number two and admit a natural description in terms of the ternary relation of betweenness in the underlying structure. We characterize a nested pair of classes of betweenness which generate convex geometries of Carathéodory number two. The corresponding antimatroids include all antimatroids arising from double shellings of partially oredred sets and all antimatroids arising from simplicial shellings of triangulated graphs. © 2009 Springer Berlin Heidelberg.