Thermodynamic depth of causal states: Objective complexity via minimal representations

1999 ◽  
Vol 59 (1) ◽  
pp. 275-283 ◽  
Author(s):  
James P. Crutchfield ◽  
Cosma Rohilla Shalizi
Keyword(s):  
Causal States ◽  
Minimal Representations

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

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Aleksander J. Cianciara ◽  
S. James Gates ◽  
Yangrui Hu ◽  
Renée Kirk
Keyword(s):  
Coxeter Groups ◽  
Auxiliary Field ◽  
Permutation Groups ◽  
Weight Space ◽  
Field Problem ◽  
Truncated Octahedron ◽  
Color Problem ◽  
Minimal Representations

Abstract 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.

scholarly journals MINIMAL REPRESENTATIONS OF LOCALLY PROJECTIVE AMALGAMS

2004 ◽  
Vol 70 (01) ◽  
pp. 142-164 ◽  
Author(s):  
A. A. IVANOV ◽  
D. V. PASECHNIK
Keyword(s):  
Minimal Representations

MINIMAL 3-BRAID REPRESENTATIONS

1994 ◽  
Vol 03 (02) ◽  
pp. 163-177 ◽  
Author(s):  
R. D. KEEVER
Keyword(s):  
Conjugacy Class ◽  
Canonical Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Minimal Representation ◽  
Class A ◽  
Minimal Representations ◽  
Necessary And Sufficient

This paper provides necessary and sufficient conditions for a representation of any 3-braid to be minimal (with regard to the number of crossings) and includes an algorithm to obtain such a representation, the number of distinct minimal representations of a given 3-braid, as well as a unique canonical form for each braid in B3. Also presented are necessary and sufficient conditions for any 3-string braid word to be a minimal representation of its conjugacy class. A canonical form for each conjugacy class in B3 is given.

The method of minimal representations in 2D Ising model calculations

1994 ◽  
Vol 114 (2) ◽  
pp. 257-264 ◽  
Author(s):  
Beresford N. Parlett ◽  
Wee-Liang Heng
Keyword(s):  
Ising Model ◽  
Model Calculations ◽  
Minimal Representations
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