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Please use this identifier to cite or link to this item: http://repository.iitr.ac.in/handle/123456789/9832
Title: A generalization of sumsets of set of integers
Authors: Mistri R.K.
Pandey R.K.
Published in: Journal of Number Theory
Abstract: Let A be a nonempty finite set of integers. The h-fold sumset of A, denoted by hA, is the set of all sums of h elements of A with repetitions allowed. A restricted h-fold sumset of A, denoted by Ä¥A, is the set of all sums of h distinct elements of A. For h ≥ 1 and r ≥ 1, we define a generalized h-fold sumset, denoted by h(r)A, which is the set of all sums of h elements of A, where each element appearing in the sum can be repeated at most r times. Thus the h-fold sumset hA and the restricted h-fold sumset Ä¥A are particular cases of the sumset h(r)A for r = h and r = 1, respectively. 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 of integers for which |h(r)A| is minimal. In this paper we solve both the problems. © 2014 Elsevier Inc.
Citation: Journal of Number Theory (2014), 143(): 334-356
URI: https://doi.org/10.1016/j.jnt.2014.04.005
http://repository.iitr.ac.in/handle/123456789/9832
Issue Date: 2014
Publisher: Academic Press Inc.
Keywords: Arithmetic progression
Direct and inverse problems
H-Fold sumsets
ISSN: 0022314X
Author Scopus IDs: 56203915400
35097679700
Author Affiliations: Mistri, R.K., Department of Mathematics, Indian Institute of Technology Patna, Patna 800013, India
Pandey, R.K., Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India
Corresponding Author: Pandey, R.K.; Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India; email: ramkpandey@gmail.com
Appears in Collections:Journal Publications [MA]

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