The Cardinality of Sumsets: Different Summands

Brendan Murphy; Eyvindur Ari Palsson; Giorgis Petridis

The Cardinality of Sumsets: Different Summands

Brendan Murphy, Eyvindur Ari Palsson, Giorgis Petridis

Pure Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

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.

Original language	English
Journal	Acta Arithmetica
Publication status	Published - 9 Sept 2013

Bibliographical note

25 pages. A minor change in the statement of Lemma 5.13

Keywords

math.CO
11B30

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title = "The Cardinality of Sumsets: Different Summands",

abstract = " 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. ",

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journal = "Acta Arithmetica",

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T2 - Different Summands

AU - Murphy, Brendan

AU - Palsson, Eyvindur Ari

AU - Petridis, Giorgis

N1 - 25 pages. A minor change in the statement of Lemma 5.13

PY - 2013/9/9

Y1 - 2013/9/9

N2 - 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.

AB - 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.

KW - math.CO

KW - 11B30

M3 - Article (Academic Journal)

SN - 0065-1036

JO - Acta Arithmetica

JF - Acta Arithmetica

ER -

The Cardinality of Sumsets: Different Summands

Abstract

Bibliographical note

Keywords

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