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.

Atomic Insights into Ti Doping on the Stability Enhancement of Truncated Octahedron LiMn2O4 Nanoparticles

Ti-doped truncated octahedron LiTixMn2-xO4 nanocomposites were synthesized through a facile hydrothermal treatment and calcination process. By using spherical aberration-corrected scanning transmission electron microscopy (Cs-STEM), the effects of Ti-doping on the structure evolution and stability enhancement of LiMn2O4 are revealed. It is found that truncated octahedrons are easily formed in Ti doping LiMn2O4 material. Structural characterizations reveal that most of the Ti4+ ions are composed into the spinel to form a more stable spinel LiTixMn2−xO4 phase framework in bulk. However, a portion of Ti4+ ions occupy 8a sites around the {001} plane surface to form a new TiMn2O4-like structure. The combination of LiTixMn2−xO4 frameworks in bulk and the TiMn2O4-like structure at the surface may enhance the stability of the spinel LiMn2O4. Our findings demonstrate the critical role of Ti doping in the surface chemical and structural evolution of LiMn2O4 and may guide the design principle for viable electrode materials.