Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/161257
Title: On the number of nonnegative sums for certain function
Authors: Ku, Cheng Yeaw
Wong, Kok Bin
Keywords: Science::Mathematics
Issue Date: 2020
Source: Ku, C. Y. & Wong, K. B. (2020). On the number of nonnegative sums for certain function. Bulletin of the Malaysian Mathematical Sciences Society, 43(1), 15-24. https://dx.doi.org/10.1007/s40840-018-0661-6
Journal: Bulletin of the Malaysian Mathematical Sciences Society 
Abstract: Let [n] = {1 , 2 , ⋯ , n}. For each i ∈ [k] and j ∈ [n], let wᵢ(j) be a real number. Suppose that ∑ i∈[k], j∈[n] wᵢ(j) ≥ 0. Let F be the set of all functions with domain [k] and codomain [n]. For each f ∈ F, let w(f) = w₁(f(1)) + w₂(f(2)) + ⋯ + wk (f(k)). A function f ∈ F is said to be nonnegative if w(f) ≥ 0. Let F⁺(w) be set of all nonnegative functions, i.e., F⁺(w) = {f ∈ F: w(f) ≥ 0}. In this paper, we show that |F⁺(w)| ≥ nᵏ⁻¹ for n ≥ 3 (k -1)².
URI: https://hdl.handle.net/10356/161257
ISSN: 0126-6705
DOI: 10.1007/s40840-018-0661-6
Schools: School of Physical and Mathematical Sciences 
Rights: © 2018 Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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