@article{Mats2007InfinitelyMI,
title={Infinitely Many Information Inequalities},
author={Frantisek Mat{\'u}s},
journal={2007 IEEE International Symposium on Information Theory},
year={2007},
pages={41-44}
}

When finite, Shannon entropies of all sub vectors of a random vector are considered for the coordinates of an entropic point in Euclidean space. A linear combination of the coordinates gives rise to an unconstrained information inequality if it is nonnegative for all entropic points. With at least four variables no finite set of linear combinations generates all such inequalities. This is proved by constructing explicitly an infinite sequence of new linear information inequalities and a curve… CONTINUE READING