Natural Vector Spaces (inward power and Minkowski norm of a Natural Vector, Natural Boolean Hypercubes) and a Fermat’s Last Theorem conjecture

• Published in: Journal of mathematical chemistry Vol. 55; no. 4; pp. 914 - 940
• Main Author: Carbó-Dorca, Ramon
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.04.2017; Springer Nature B.V
• Subjects: Boolean algebra; Chemistry; Chemistry and Materials Science; Hypercubes; Math. Applications in Chemistry; Molecular structure; Norms; Number theory; Original Paper; Physical Chemistry; Similarity; Theorems; Theoretical and Computational Chemistry; Vector spaces; Inward vector powers; Minkowski norms; Fermat’s Last Theorem; Fermat Natural Vectors; Quantum molecular similarity; Fermat discrete probability distributions; Complete vector sums; Natural Vector Semispaces
• ISSN: 0259-9791; 1572-8897
• DOI: 10.1007/s10910-016-0708-6

In order to use the structure and operations of Molecular Similarity semispaces, Natural Vector Semispaces are considered in this study as vector spaces defined over the set of natural numbers, with zero added if necessary. The complete sum and inward power of a vector, defined as basic tools in Quantum Molecular Similarity, are now applied to a Natural Vector to describe Minkowski norms in these vector spaces. The structure and behavior of the Minkowski norm of Natural Vector inward powers and the Boolean Hypercube vertex translation into natural numbers are further used to conjecture a plausible general set up of Fermat’s Last Theorem.