Eprints of Rényi Institute

Book inequalities

Csirmaz, László (2013) Book inequalities. Not submitted . (Submitted)

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Abstract

Information theoretical inequalities have strong ties with polymatroids and their representability. A polymatroid is entropic if its rank function is given by the Shannon entropy of the subsets of discrete random variables. As observed by Zhang and Yeung, entropic polymatroids are closed under adhesive extensions which property can be used to obtain new information inequalities. The book is a special iterated adhesive extension of a polymatroid. F. Matus proved that a polymatroid has a 2-page book extension if and only if it satisfies six Zhang-Yeung inequalities. Using computer aided multiobjective optimization we give a complete characterization of four element polymatroids which admit up to 9 page book extension. Based on these results a conjecture is formulated which describes all non-Shannon information inequalities, called book inequalities, yielded by book extensions.

Item Type:Article
Keywords and phrases:Entropy; information inequalities; polymatroid; adhesivity
Subjects:52B12 Special polytopes (linear programming, centrally symmetric, etc.)
90C29 Multi-objective and goal programming
05B35 Matroids, geometric lattices
94A17 Measures of information, entropy
Divisions:Research Groups > Theoretical cryptography
Last Modified:03 Oct 2013 16:07

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