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A Refinement of the Conjecture on the Pseudo Component Transformation of the Lattice Points in the Simplex

Authors
Kim, BaraKim, Jeongsim
Issue Date
9월-2020
Publisher
MDPI
Keywords
mixture experiments; lattice points; pseudo component transformation
Citation
SYMMETRY-BASEL, v.12, no.9
Indexed
SCIE
SCOPUS
Journal Title
SYMMETRY-BASEL
Volume
12
Number
9
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/53228
DOI
10.3390/sym12091427
ISSN
2073-8994
Abstract
We consider mixture experiments in which the proportions of the components must be non-negative and their sum must equal one. Thus, the experimental region for a mixture of components is a simplex. Li and Zhang (2017) made the conjecture that the pseudo component transformation of the lattice points in the simplex has a special property. In this paper, we show that this conjecture is not true in general. Furthermore, we refine this conjecture and prove the refined conjecture.
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