Projections, entropy and sumsets


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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Correspondence to Béla Bollobás.

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Research supported in part by NSF grants CCR-0225610, DMS-0505550 and W911NF-06-1-0076

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Balister, P., Bollobás, B. Projections, entropy and sumsets. Combinatorica 32, 125–141 (2012).

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Mathematics Subject Classification (2000)

  • 52B60
  • 11P99