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A Refinement of the Conjecture on the Pseudo Component Transformation of the Lattice Points in the Simplex
Bara Kim
and
Jeongsim Kim
*
Version 1
: Received: 20 August 2020 / Approved: 20 August 2020 / Online: 20 August 2020 (08:07:43 CEST)
How to cite: Kim, B.; Kim, J. A Refinement of the Conjecture on the Pseudo Component Transformation of the Lattice Points in the Simplex. Preprints 2020, 2020080444 Kim, B.; Kim, J. A Refinement of the Conjecture on the Pseudo Component Transformation of the Lattice Points in the Simplex. Preprints 2020, 2020080444
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.
Subject Areas
mixture experiments; lattice points; pseudo component transformation
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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