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Please use this identifier to cite or link to this item: http://repository.iitr.ac.in/handle/123456789/9831
Title: A generalization of sumset and its applications
Authors: Mistri R.K.
Pandey R.K.
Prakash O.
Published in: Proceedings of the Indian Academy of Sciences: Mathematical Sciences
Abstract: Let A be a nonempty finite subset of an additive abelian group G and let r and h be positive integers. The generalized h-fold sumset of A, denoted by h( r )A, is the set of all sums of h elements of A, where each element appears in a sum at most r times. The direct problem for h( r )A is to find a lower bound for | h( r )A| in terms of |A|. The inverse problem for h( r )A is to determine the structure of the finite set A for which | h( r )A| is minimal with respect to some fixed value of |A|. If G= Z, the direct and inverse problems are well studied. In case of G= Z/ pZ, p a prime, the direct problem has been studied very recently by Monopoli (J. Number Theory, 157 (2015) 271–279). In this paper, we express the generalized sumset h( r )A in terms of the regular and restricted sumsets. As an application of this result, we give a new proof of the theorem of Monopoli and as the second application, we present new proofs of direct and inverse theorems for the case G= Z. © 2018, Indian Academy of Sciences.
Citation: Proceedings of the Indian Academy of Sciences: Mathematical Sciences (2018), 128(5): -
URI: https://doi.org/10.1007/s12044-018-0437-9
http://repository.iitr.ac.in/handle/123456789/9831
Issue Date: 2018
Publisher: Springer
Keywords: Arithmetic progression
direct and inverse problems
h-fold sumsets
ISSN: 2534142
Author Scopus IDs: 56203915400
35097679700
57210722800
Author Affiliations: Mistri, R.K., Department of Mathematics, Harish-Chandra Research Institute, Allahabad, 211 019, India
Pandey, R.K., Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247 667, India
Prakash, O., Department of Mathematics, Indian Institute of Technology Patna, Patna, 800 013, India
Corresponding Author: Pandey, R.K.; Department of Mathematics, Indian Institute of Technology RoorkeeIndia; email: ramkpandey@gmail.com
Appears in Collections:Journal Publications [MA]

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