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Title: On the number of nonnegative sums for semi-partitions
Authors: Ku, Cheng Yeaw
Wong, Kok Bin
Keywords: Science::Mathematics
Issue Date: 2021
Source: Ku, C. Y. & Wong, K. B. (2021). On the number of nonnegative sums for semi-partitions. Graphs and Combinatorics, 37(6), 2803-2823.
Journal: Graphs and Combinatorics
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 ∑X∈([n]k)w(X)≥0. Let Un,t,k be the set of all P= { P1, P2, ⋯ , Pt} such that Pi∈([n]k) for all i and Pi∩ Pj= ∅ for i≠ j. For each P∈ Un,t,k, let w(P) = ∑ P∈Pw(P). Let Un,t,k+(w) be set of all P∈ Un,t,k with w(P) ≥ 0. In this paper, we show that |Un,t,k+(w)|≥∏1≤i≤(t-1)k(n-tk+i)(k!)t-1((t-1)!) for sufficiently large n.
ISSN: 0911-0119
DOI: 10.1007/s00373-021-02393-8
Schools: School of Physical and Mathematical Sciences 
Rights: © 2021 The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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