English

Entropy Functions on Two-Dimensional Faces of Polymatroid Region with One Extreme Ray Containing Rank-One Matroid

Information Theory 2026-02-04 v1 math.IT

Abstract

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.

Keywords

Cite

@article{arxiv.2602.03363,
  title  = {Entropy Functions on Two-Dimensional Faces of Polymatroid Region with One Extreme Ray Containing Rank-One Matroid},
  author = {Kaizhe He and Qi Chen},
  journal= {arXiv preprint arXiv:2602.03363},
  year   = {2026}
}