Entropic regions and matroids

2010. december 9. csütörtök 16:15

The Shannon entropies of all subvectors of a random vector are considered for the coordinates of an entropic point in a Euclidean space. The entropic points in a space define an entropic region. The problem to describe the region will be reviewed and connections to the matroid theory discussed. Two classes of matroids are closely related: partition representable and asymptotically entropic. A matroid is partition representable if its rank function is a multiple of an entropic point. A matroid is asymptotically entropic if its rank function is in the closure of the entropic region.