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Please use this identifier to cite or link to this item: http://repository.iitr.ac.in/handle/123456789/10667
Title: Subsequence sums: Direct and inverse problems
Authors: Mistri R.K.
Pandey R.K.
Praksh O.
Published in: Journal of Number Theory
Abstract: Let A=(a0,. . .,a0,r0copies,a1,. . .,a1,r1copies,. . .,ak-1,. . .,ak-1,rk-1copies) be a finite sequence of integers with k distinct terms, denoted alternatively by (a0,a1,. . .,ak-1)r, where a0<a1<..<ak-1, r=(r0,r1,. . .,rk-1), ri≥1 for i=0, 1, . . ., k-1. The sum of all the terms of a subsequence of length at least one of the sequence A is said to be a subsequence sum of A. The set of all subsequence sums of A is denoted by S(r,A). The direct problem for subsequence sums is to find the lower bound for |S(r,A)| in terms of the number of distinct terms in the sequence A. The inverse problem for subsequence sums is to determine the structure of the finite sequence A of integers for which |S(r,A)| is minimal. In this paper, both the problems are solved and some well-known results for subset sum problem are obtained as corollaries of the results for subsequence sum problem. © 2014 Elsevier Inc.
Citation: Journal of Number Theory (2015), 148(): 235-256
URI: https://doi.org/10.1016/j.jnt.2014.09.010
http://repository.iitr.ac.in/handle/123456789/10667
Issue Date: 2015
Publisher: Academic Press Inc.
Keywords: Direct problems
Inverse problems
Subsequence sums
Subset sums
ISSN: 0022314X
Author Scopus IDs: 56203915400
35097679700
56412020400
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
Praksh, O., Department of Mathematics, Indian Institute of Technology Patna, Patna, 800013, India
Corresponding Author: Pandey, R.K.; Department of Mathematics, Indian Institute of Technology RoorkeeIndia
Appears in Collections:Journal Publications [MA]

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