Working Paper Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 20 August 2020 / Approved: 20 August 2020 / Online: 20 August 2020 (08:07:54 CEST)

A peer-reviewed article of this Preprint also exists.

Kim, B.; Kim, J. A Refinement of the Conjecture on the Pseudo Component Transformation of the Lattice Points in the Simplex. Symmetry 2020, 12, 1427. Kim, B.; Kim, J. A Refinement of the Conjecture on the Pseudo Component Transformation of the Lattice Points in the Simplex. Symmetry 2020, 12, 1427.

Journal reference: Symmetry 2020, 12, 1427
DOI: 10.3390/sym12091427

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

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