0085051 - ÚTIA 2008 RIV US eng J - Journal Article
Matúš, František
Two constructions on limits of entropy functions.
[Dvě konstrukce na limitách entropických funkcí.]
IEEE Transactions on Information Theory. Roč. 53, č. 1 (2007), s. 320-330. ISSN 0018-9448. E-ISSN 1557-9654
R&D Projects: GA AV ČR IAA100750603
Institutional research plan: CEZ:AV0Z10750506
Keywords : almost affine code * coloring * equipartition * ideal secret sharing * information inequalities * polymatroid
Subject RIV: BA - General Mathematics
Impact factor: 2.315, year: 2007

The correspondence between the subvectors of a random vector and their Shannon entropies gives rise to an entropy function. Limits of the entropy functions are closed to convolutions with modular polymatroids, and when integer-valued also to free expansions. The problem of description of the limits of entropy functions is reduced to those limits that correspond to matroids. Related results on entropy functions are reviewed with regard to polymatroid and matroid theories, and perfect and ideal secret sharing.

Entropická funkce přiřazuje podvektorům náhodného vektoru jejich Shannovy entropie. Limity entropických funkcí jsou uzavřeny na konvoluce s modulárními polymatroidy a na volné expanze, pokud jsou celočíselné. Fundamentální problém popisu limit entropických funkcí je redukován na ty limity, které odpovídají matroidům.
Permanent Link: http://hdl.handle.net/11104/0147641