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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 â‰¥ 1 and r â‰¥ 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. Â© 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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