Rank functions of strict cg-matroids

A matroid-like structure defined on a convex geometry, called a cg-matroid, is defined by Fujishige et al. [Matroids on convex geometries (cg-matroids), Discrete Math. 307 (2007) 1936-1950]. A cg-matroid whose rank function is naturally defined is called a strict cg-matroid. In this paper, we give characterizations of strict cg-matroids by their rank functions.