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.

翻译：熵函数的刻画在信息论中具有基础重要性。通过对香农外边界（即多拟阵区域）施加约束，可获得该区域的各个面以及具有特殊结构的熵函数。本文刻画了由一个拟阵与一个秩一拟阵张成的n次多拟阵区域的二维面上的熵函数，并将所有此类二维面分为四种类型。