Bibliography

(eng): When finite, Shannon entropies of all subvectors 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 in a special geometric position to the half/-spaces defined by the inequalities. The inequalities are constructed recurrently by adhesive pasting of restrictions of polymatroids and the curve ranges in the closure of a set of the entropic points.

(cze): Byly nalezeny nekonečné posloupnosti nových infomačních nerovností mezi čtyřmi náhodnými veličinami a dokázáno, že kužel limit entropických funkcí není konečně generovaný, pro nejméně čtyřy veličiny.