Non-isomorphic distribution supports for calculating entropic vectors

A 2^N - 1 dimensional vector is said to be entropic if each of its entries can be regarded as the joint entropy of a particular subset of N discrete random variables. The explicit characterization of the closure of the region of entropic vectors Γ̅*_N is unknown for N ≥ 4. A systematic approach is proposed to generate the list of non-isomorphic distribution supports for the purpose of calculating and optimizing entropic vectors. It is shown that a better understanding of the structure of the entropy region can be obtained by constructing inner bounds based on these supports. The constructed inner bounds based on different supports are compared both in full dimension and in a transformed three dimensional space of Csirmaz and Matúš.