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Publication - Dr Brendan Murphy

    The Cardinality of Sumsets

    Different Summands


    Murphy, B, Palsson, EA & Petridis, G, 2013, ‘The Cardinality of Sumsets: Different Summands’. Acta Arithmetica.


    Let $h$ be a positive integer and $A, B_1, B_2,\dots, B_h$ be finite sets in a commutative group. We bound $|A+B_1+...+B_h|$ from above in terms of $|A|, |A+B_1|,\dots,|A+B_h|$ and $h$. Extremal examples, which demonstrate that the bound is asymptotically sharp in all the parameters, are furthermore provided.

    Full details in the University publications repository