The cardinality of sumsets: different summands

Brendan Murphy, Eyvindur Ari Palsson, and Giorgis Petridis. "The cardinality of sumsets: different summands." Acta Arithmetica 167.4 (2015): 375-395. <http://eudml.org/doc/279673>.

@article{BrendanMurphy2015,
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 $A, B₁, ..., B_h$ 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.},
author = {Brendan Murphy, Eyvindur Ari Palsson, Giorgis Petridis},
journal = {Acta Arithmetica},
keywords = {sumsets; Plünnecke graphs; square commutative graphs},
language = {eng},
number = {4},
pages = {375-395},
title = {The cardinality of sumsets: different summands},
url = {http://eudml.org/doc/279673},
volume = {167},
year = {2015},
}

TY - JOUR
AU - Brendan Murphy
AU - Eyvindur Ari Palsson
AU - Giorgis Petridis
TI - The cardinality of sumsets: different summands
JO - Acta Arithmetica
PY - 2015
VL - 167
IS - 4
SP - 375
EP - 395
AB - 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.
LA - eng
KW - sumsets; Plünnecke graphs; square commutative graphs
UR - http://eudml.org/doc/279673
ER -