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Generator Pairs for all 4x4 GF(2) Representations of S4
There are nine conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices. This report gives generator matrices for one group in each class. These generator pairs allow each of the ...
A Universal Symmetry Detection Algorithm
Research on symmetry detection focuses on identifying and detecting new types of symmetry. We present an algorithm that is capable of detecting any type of permutation based symmetry, including many types for which there ...
Conjugates of the Standard Representation of S3 in 3x3 matrices
This is a list of the 28 conjugates of the standard representation of S3 in 3x3 matrices.
The Number of Conjugates of the Standard Representation of Sn in the General Linear Group over GF(2)
This report determines the normalizer of the standard representation of Sn in the general linear group of nxn matrices over GF(2). The size of the normalizer is then used to determine the number of classes of conjugate ...
Super symmetry is a type of matrix-based symmetry that extends the concept of total symmetry. Super symmetric functions are “even more symmetric” than totally symmetric functions. Even if a function is not super ...
The Super Symmetric Representations of S4 in GL3(2)
This report gives all conjugacy classes of the super symmetric groups HR3 and VR3