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

Bara Kim, Jeongsim Kim

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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 languageEnglish
Article number1427
JournalSymmetry
Volume12
Issue number9
DOIs
Publication statusPublished - 2020 Sept

Bibliographical note

Funding Information:
Funding: B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2B5B01001864). J. Kim’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:
© 2020 by the authors.

Keywords

  • Lattice points
  • Mixture experiments
  • Pseudo component transformation

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • General Mathematics
  • Physics and Astronomy (miscellaneous)

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