Some intersection theorems for ordered sets and graphs
Journal of Combinatorial Theory Series A
Elements of information theory
Elements of information theory
Random Structures & Algorithms - Proceedings of the Thirteenth International Conference “Random Structures and Algorithms” held May 28–June 1, 2007, Tel Aviv, Israel
Information inequalities for joint distributions, with interpretations and applications
IEEE Transactions on Information Theory
Sumset and inverse sumset theory for shannon entropy
Combinatorics, Probability and Computing
Two Constructions on Limits of Entropy Functions
IEEE Transactions on Information Theory
Generalized Entropy Power Inequalities and Monotonicity Properties of Information
IEEE Transactions on Information Theory
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A new notion of partition-determined functions is introduced, and several basic inequalities are developed for the entropies of such functions of independent random variables, as well as for cardinalities of compound sets obtained using these functions. Here a compound set means a set obtained by varying each argument of a function of several variables over a set associated with that argument, where all the sets are subsets of an appropriate algebraic structure so that the function is well defined. On the one hand, the entropy inequalities developed for partition-determined functions imply entropic analogues of general inequalities of Plünnecke-Ruzsa type. On the other hand, the cardinality inequalities developed for compound sets imply several inequalities for sumsets, including for instance a generalization of inequalities proved by Gyarmati, Matolcsi and Ruzsa (2010). We also provide partial progress towards a conjecture of Ruzsa (2007) for sumsets in nonabelian groups. All proofs are elementary and rely on properly developing certain information-theoretic inequalities. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 399–424, 2012 © 2012 Wiley Periodicals, Inc.