The cardinality of sumsets: different summands

Thomas Brendan Murphy, Eyvindur A. Palsson, Giorgis Petridis

Type: Article

Publication Date: 2015-01-01

Citations: 1

DOI: https://doi.org/10.4064/aa167-4-4

Abstract

We offer a complete answer to the following question on the growth of sumsets in commutative groups. Let $h$ be a positive integer and $A, B_1, \dots , B_h$ be finite sets in a commutative group. We bound $|A+B_1+\dots +B_h|$ from above in terms of $|A|$,

Locations

Acta Arithmetica - View - PDF
arXiv (Cornell University) - View - PDF

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Works Cited by This (8)

Action	Title	Year	Authors
+	An Application of Graph Theory to Additive Number Theory	1985	Noga Alon P. Erdős
+ PDF Chat	A superadditivity and submultiplicativity property for cardinalities of sumsets	2010	Katalin Gyarmati Máté Matolcsi Imre Z. Ruzsa
+	Projections of Bodies and Hereditary Properties of Hypergraphs	1995	Béla Bollobás Andrew Thomason
+ PDF Chat	Projections, entropy and sumsets	2012	Paul Balister Béla Bollobás
+	Additive number theory: inverse problems and the geometry of sumsets	1997	Melvyn B. Nathanson
+	Cardinality questions about sumsets	2007	Imre Z. Ruzsa
+ PDF Chat	Upper bounds on the cardinality of higher sumsets	2013	Giorgis Petridis
+ PDF Chat	Entropy and set cardinality inequalities for partition‐determined functions	2011	Mokshay Madiman Adam W. Marcus Prasad Tetali