Entropy Functions on Two-Dimensional Faces of Polymatroid Region Spanned by a Matroid and a Rank-One Matroid

Characterization of entropy functions is of fundamental importance in information theory. By imposing constraints on their Shannon outer bound, i.e., the polymatroidal region, one obtains the faces of the region and entropy functions on them with special structures. In this paper, we characterize entropy functions on 2-dimensional faces of polymatroidal region of degree n spanned by a matroid and a rank-1 matroid. We classify all such 2-dimensional faces into four types.