Transfer matrix in counting problems

The transfer matrix is a powerful technique that can be applied to statistical mechanics systems as, for example, in the calculus of the entropy of the ice model. One interesting way to study such systems is to map it onto a three-color problem. In this paper, we explicitly build the transfer matrix for the three-color problem in order to calculate the number of possible configurations for finite systems with free, periodic in one direction and toroidal boundary conditions (periodic in both directions)

The 300 “correlators” suggests 4D, $$ \mathcal{N} $$ = 1 SUSY is a solution to a set of Sudoku puzzles

A conjecture is made that the weight space for 4D, $$ \mathcal{N} $$ N -extended supersymmetrical representations is embedded within the permutahedra associated with permutation groups 𝕊d. Adinkras and Coxeter Groups associated with minimal representations of 4D, $$ \mathcal{N} $$ N = 1 supersymmetry provide evidence supporting this conjecture. It is shown that the appearance of the mathematics of 4D, $$ \mathcal{N} $$ N = 1 minimal off-shell supersymmetry representations is equivalent to solving a four color problem on the truncated octahedron. This observation suggest an entirely new way to approach the off-shell SUSY auxiliary field problem based on IT algorithms probing the properties of 𝕊d.

Generalized 2N Color Theorem

2N-Color Theorem This article gives a standard proof of the famous Four-Color theorem and generalizes it be the 2N-Color problem. The article gives a number of possible applications of the 2N-Color problem that is the essence of orientation. Orientation is fundamental to many fields of scientific knowledge. The Fourcolor theorem applies to map making by the knowledge that only four colors are necessary to color a planar map. The Six-color theorem applies to three dimensional space implying that a space station could be ideally designed to have six compartments adjacent to one another allowing a door from any one of the compartments to the other five. The 2N-color generalization applies to the physical reality of quantum physics. Bubble chamber investigations suggest that the universe is four or more dimensions. Thus the 2N-color theorem applies to the N dimensional universe. At this time string theorists have suggested that the universe could be greater than four dimensions. Physics has not as of yet proven the exact dimension of the universe that could even be infinite as a possibility

Colors challenges in navigating autonomous vehicles

Will autonomous vehicles ever be able to drive around safely? In Germany lane markers on streets are white. In construction zones temporary markers are installed on top of the standard ones that are yellow and they direct the traffic e.g. into shifted lanes. So, the only differentiation is the color. But what about the white markers at times close to the sunset? Then we drive into Austria and the temporary markers are turning orange. Or driving in the US makes the whole country a construction zone because markers are always yellow. Automotive cameras are often times not RGB cameras. They have other color filters to maximize sensitivity, which often times does not help differentiating colors. So does the spectral reflectance matter? Which impact does the illumination have? And there are many different ones like daylight at different times of the day, different kinds of streetlights, different headlights of the cars etc. Traffic signs create another color problem. We drive from Switzerland to France. In Switzerland the freeway signs are green and the major road signs are blue. When you cross the French border, it is the other way around. How can these problems be solved?