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 polymatroid region of degree n with one extreme ray containing rank-1 matroid. We classify all such 2-dimensional faces with another extreme ray containing a matroid into four types.

翻译：熵函数的表征在信息论中具有基础性重要性。通过对香农外边界（即多拟阵区域）施加约束，可获得该区域的各类面及其上具有特殊结构的熵函数。本文针对n阶多拟阵区域中某极端射线包含秩为一拟阵的二维面，系统刻画了其上的熵函数。通过将另一极端射线包含拟阵的所有此类二维面划分为四种类型，实现了完整的分类。