Department of
Applied
Mathematics

Matroids represented by entropies

Frantisek Matus

UTIA AV

Abstract

A matroid is partition representable if its rank function corresponds to the collection of Shannon entropies of all subvectors of a random vector. A matroid is asymptotically entropic if its rank function is a limit of such collections. Results on and open problems related to these two classes of matroids will be reviewed. Connections to almost affine codes, ideal secret sharing schemes and entropic regions, studied in information theory, will be outlined.