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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 ...
Anti-Symmetry and Logic Simulation
Like ordinary symmetries, anti-symmetries are defined in terms of relations between function cofactors. For ordinary symmetries, two cofactors must be equal, for anti-symmetries two cofactors must be complements of ...
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 ...
Extending Symmetric Variable-Pair Transitivities Using State-Space Transformations
Two-cofactor relations and their associated symmetry types have been studied for many years. While ordinary symmetries are simply transitive permitting them to be combined into clusters of variables, other types of symmetries ...
Why is Symmetry So Hard?
The problem of detecting virtually any type of symmetry is shown to be co-NP-complete. We start with totally symmetric functions, then extend the result to partially symmetric functions, then to more general cofactor ...