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

• Autorzy: David B. Penman , Matthew D. Wells
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11B75: Other combinatorial number theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 165
• Numer: 4
• Strony: 361-383

Daty

wydano

2014

Twórcy

autor

David B. Penman

• Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, United Kingdom

autor

Matthew D. Wells

• Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, United Kingdom

Identyfikatory

DOI

10.4064/aa165-4-6