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arXiv · 0810.1488

Plunnecke's inequality for different summands

Katalin Gyarmati·Mate Matolcsi·Imre Z. Ruzsa
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Abstract

The aim of this paper is to prove a general version of Plünnecke's inequality. Namely, assume that for finite sets $A$, $B_1, ... B_k$ we have information on the size of the sumsets $A+B_{i_1}+... +B_{i_l}$ for all choices of indices $i_1, ... i_l.$ Then we prove the existence of a non-empty subset $X$ of $A$ such that we have `good control' over the size of the sumset $X+B_1+... +B_k$. As an application of this result we generalize an inequality of \cite{gymr} concerning the submultiplicativity of cardinalities of sumsets.

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Katalin Gyarmati, Mate Matolcsi, Imre Z. Ruzsa. 2008-10-08. Plunnecke's inequality for different summands. https://arxiv.org/abs/0810.1488

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