A refinement of the conjecture on the pseudo component transformation of the lattice points in the simplex

Bara Kim; Jeongsim Kim

doi:10.3390/SYM12091427

A refinement of the conjecture on the pseudo component transformation of the lattice points in the simplex

Bara Kim, Jeongsim Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Article number	1427
Journal	Symmetry
Volume	12
Issue number	9
DOIs	https://doi.org/10.3390/SYM12091427
Publication status	Published - 2020 Sept

Keywords

Lattice points
Mixture experiments
Pseudo component transformation

ASJC Scopus subject areas

Computer Science (miscellaneous)
Chemistry (miscellaneous)
Mathematics(all)
Physics and Astronomy (miscellaneous)

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title = "A refinement of the conjecture on the pseudo component transformation of the lattice points in the simplex",

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.",

keywords = "Lattice points, Mixture experiments, Pseudo component transformation",

author = "Bara Kim and Jeongsim Kim",

note = "Funding Information: Funding: B. Kim{\textquoteright}s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2B5B01001864). J. Kim{\textquoteright}s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01065568) and was conducted during the research year of Chungbuk National University in 2020. Publisher Copyright: {\textcopyright} 2020 by the authors.",

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PY - 2020/9

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N2 - 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.

AB - 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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JO - Symmetry

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ER -

A refinement of the conjecture on the pseudo component transformation of the lattice points in the simplex

Abstract

Keywords

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