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Upper bounds on the cardinality of higher sumsets

100%

Petridis G.

Acta Arithmetica

2013

tom 158

nr 4

299-319

Let A and B be finite sets in a commutative group. We bound |A+hB| in terms of |A|, |A+B| and h. We provide a submultiplicative upper bound that improves on the existing bound of Imre Ruzsa by inserting a factor that decreases with h.

The cardinality of sumsets: different summands

51%

Murphy B., Palsson E., Petridis G.

Acta Arithmetica

2015

tom 167

nr 4

375-395

We offer a complete answer to the following question on the growth of sumsets in commutative groups. Let h be a positive integer and $A, B₁, ..., B_h$ be finite sets in a commutative group. We bound $|A + B₁ + ... + B_h|$ from above in terms of |A|, |A + B₁|, ..., $|A + B_h|$ and h. Extremal examples, which demonstrate that the bound is asymptotically sharp in all parameters, are furthermore provided.

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2 Acta Arithmetica

2 Petridis G.

1 Murphy B.

1 Palsson E.

1 2015

1 2013

Wyniki wyszukiwania

Upper bounds on the cardinality of higher sumsets

The cardinality of sumsets: different summands