Symmetric Entropy Regions of Degrees Six and Seven

TL;DR

This paper classifies G-symmetric almost entropic regions for degrees six and seven based on their Shannon-tightness, determining whether they can be fully characterized by Shannon-type inequalities.

Contribution

It provides a complete classification of G-symmetric almost entropic regions for degrees six and seven, focusing on Shannon-tightness.

Findings

Classification of G-symmetric almost entropic regions for degrees six and seven

Identification of Shannon-tight and non-tight regions within these classifications

Advancement in understanding the structure of entropic regions under symmetry constraints

Abstract

In this paper, we classify all G-symmetric almost entropic regions according to their Shannon-tightness, that is, whether they can be fully characterized by Shannon-type inequalities, where G is a permutation group of degree 6 or 7.