# Sum-dominant sets and restricted-sum-dominant sets in finite abelian groups

Acta Arithmetica (2014)

• Volume: 165, Issue: 4, page 361-383
• ISSN: 0065-1036

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## Abstract

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We call a subset A of an abelian group G sum-dominant when |A+A| > |A-A|. If |A⨣A| > |A-A|, where A⨣A comprises the sums of distinct elements of A, we say A is restricted-sum-dominant. In this paper we classify the finite abelian groups according to whether or not they contain sum-dominant sets (respectively restricted-sum-dominant sets). We also consider how much larger the sumset can be than the difference set in this context. Finally, generalising work of Zhao, we provide asymptotic estimates of the number of restricted-sum-dominant sets in finite abelian groups under mild conditions.

## How to cite

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David B. Penman, and Matthew D. Wells. "Sum-dominant sets and restricted-sum-dominant sets in finite abelian groups." Acta Arithmetica 165.4 (2014): 361-383. <http://eudml.org/doc/279778>.

@article{DavidB2014,
abstract = {We call a subset A of an abelian group G sum-dominant when |A+A| > |A-A|. If |A⨣A| > |A-A|, where A⨣A comprises the sums of distinct elements of A, we say A is restricted-sum-dominant. In this paper we classify the finite abelian groups according to whether or not they contain sum-dominant sets (respectively restricted-sum-dominant sets). We also consider how much larger the sumset can be than the difference set in this context. Finally, generalising work of Zhao, we provide asymptotic estimates of the number of restricted-sum-dominant sets in finite abelian groups under mild conditions.},
author = {David B. Penman, Matthew D. Wells},
journal = {Acta Arithmetica},
keywords = {sum-dominant set; restricted-sum-dominant set; finite abelian group},
language = {eng},
number = {4},
pages = {361-383},
title = {Sum-dominant sets and restricted-sum-dominant sets in finite abelian groups},
url = {http://eudml.org/doc/279778},
volume = {165},
year = {2014},
}

TY - JOUR
AU - David B. Penman
AU - Matthew D. Wells
TI - Sum-dominant sets and restricted-sum-dominant sets in finite abelian groups
JO - Acta Arithmetica
PY - 2014
VL - 165
IS - 4
SP - 361
EP - 383
AB - We call a subset A of an abelian group G sum-dominant when |A+A| > |A-A|. If |A⨣A| > |A-A|, where A⨣A comprises the sums of distinct elements of A, we say A is restricted-sum-dominant. In this paper we classify the finite abelian groups according to whether or not they contain sum-dominant sets (respectively restricted-sum-dominant sets). We also consider how much larger the sumset can be than the difference set in this context. Finally, generalising work of Zhao, we provide asymptotic estimates of the number of restricted-sum-dominant sets in finite abelian groups under mild conditions.
LA - eng
KW - sum-dominant set; restricted-sum-dominant set; finite abelian group
UR - http://eudml.org/doc/279778
ER -

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