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

David B. Penman; Matthew D. Wells

Acta Arithmetica (2014)

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

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topDavid 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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