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Title: | Subsequence sums: Direct and inverse problems |

Authors: | Mistri R.K. Pandey, Ram Krishna 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), riâ‰¥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. Â© 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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