Open Access
2016 About New Internal Symmetries of the Integer Lattice ($\mathrm{Z^N}$)
A. Kornyushkin
J. Phys. Math. 7(2): 1-13 (2016). DOI: 10.4172/2090-0902.1000178


The numerous internal symmetries are found in N-dimensional integer lattices ($\mathrm{Z^N}$). The relation of these symmetries with the new mathematical category named the Masks (or Neighborhoods) is shown. A set of definitions for the Correct Masks and Perfect Masks is presented; the identity between the Correct and Perfect Masks is hypothesized. The relationship between the Perfection of the Mask and the new category named “Mathematical String” is shown. The Correctness of the several Masks in $\mathrm{Z^N}$ (N=1,2) is proven and a simple method to find the Correctness for all other N is outlined. The hypothesis of high population density of Perfect Masks in integer lattices $\mathrm{Z^N}$ with large N is stated.


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A. Kornyushkin. "About New Internal Symmetries of the Integer Lattice ($\mathrm{Z^N}$)." J. Phys. Math. 7 (2) 1 - 13, 2016.


Published: 2016
First available in Project Euclid: 31 August 2017

Digital Object Identifier: 10.4172/2090-0902.1000178

Keywords: Integer lattice , symmetries

Rights: Copyright © 2016 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.7 • No. 2 • 2016
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