Abstract
In this paper we shall generalize Shearer’s entropy inequality and its recent extensions by Madiman and Tetali, and shall apply projection inequalities to deduce extensions of some of the inequalities concerning sums of sets of integers proved recently by Gyarmati, Matolcsi and Ruzsa. We shall also discuss projection and entropy inequalities and their connections.
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Research supported in part by NSF grants CCR-0225610, DMS-0505550 and W911NF-06-1-0076