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Please use this identifier to cite or link to this item: http://repository.iitr.ac.in/handle/123456789/10132
Title: Direct and inverse theorems on signed sumsets of integers
Authors: Bhanja J.
Pandey R.K.
Published in: Journal of Number Theory
Abstract: Let G be an additive abelian group and h be a positive integer. For a nonempty finite subset A={a0,a1,…,ak−1} of G, we let h+_A:={Σi=0 k−1λiai:(λ0,…,λk−1)∈Zk,Σi=0 k−1|λi|=h}, be the h-fold signed sumset of A. The direct problem for the signed sumset h+_A is to find a nontrivial lower bound for |h+_A| in terms of |A|. The inverse problem for h+_A is to determine the structure of the finite set A for which |h+_A| is minimal. In this article, we solve both the direct and inverse problems for |h+_A|, when A is a finite set of integers. © 2018 Elsevier Inc.
Citation: Journal of Number Theory (2019), 196(): 340-352
URI: https://doi.org/10.1016/j.jnt.2018.09.005
http://repository.iitr.ac.in/handle/123456789/10132
Issue Date: 2019
Publisher: Academic Press Inc.
Keywords: Direct and inverse problems
Signed sumset
Sumset
ISSN: 0022314X
Author Scopus IDs: 8863572900
35097679700
Author Affiliations: Bhanja, J., Department of Mathematics, Indian Institute of Technology Roorkee, Uttarakhand, 247667, India
Pandey, R.K., Department of Mathematics, Indian Institute of Technology Roorkee, Uttarakhand, 247667, India
Funding Details: The second author would like to thank to the Indian Institute of Technology Roorkee for providing the grant to carry out the research with Grant No. MAT/FIG/100656 . We are thankful to anonymous referee for giving his/her valuable comments on the paper.
Corresponding Author: Pandey, R.K.; Department of Mathematics, Indian Institute of Technology RoorkeeIndia; email: ramkpfma@iitr.ac.in
Appears in Collections:Journal Publications [MA]

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