Ku, Cheng Yeaw and Wong, Kok Bin
(2021)
*On the number of nonnegative sums for semi-partitions.*
Graphs and Combinatorics, 37 (6).
pp. 2803-2823.
ISSN 0911-0119,
DOI https://doi.org/10.1007/s00373-021-02393-8.

## Abstract

Let n] = {1, 2,..., n}. Let (n] k) be the family of all subsets of n] of size k. Define a real-valued weight function w on the set n] k such that Sigma(X is an element of)(n] k) w( X) >= 0. Let U-n,U- t,U-k be the set of all P = {P-1, P-2,..., P-t} such that P-i. is an element of (n] k) for all i and P-i n P-j = O for i not equal j. For each P is an element of U-n,U- t,U-k, let w(P) = P is an element of P w( P). Let U+ n,t,k(w) be set of all P is an element of U-n,U- t,U-k with w(P) >= 0. In this paper, we showthat vertical bar U-n,t,k(+) (w)vertical bar >=Pi(1=i=(t-1)k) (n-tk+i)/(k!)t-1((t-1)!) for sufficiently large n.

Item Type: | Article |
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Funders: | UNSPECIFIED |

Uncontrolled Keywords: | Subset sums; Extremal problems; Partitions |

Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Science > Institute of Mathematical Sciences |

Depositing User: | Ms Zaharah Ramly |

Date Deposited: | 09 Jun 2022 07:02 |

Last Modified: | 09 Jun 2022 07:02 |

URI: | http://eprints.um.edu.my/id/eprint/27571 |

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