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 ...
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 ...
The Ontological Discovery Environment (ODE) provides an efficient structure for storage of gene and pheno-
type relations. The relations can be represented by a bipartite graph, where the gene and phenotype items
can be ...
The detailed design document covers the basic theory, related technique, and
implementation details of the MovieOracle system. It first provides a high-level system
overview. Then it discusses the usage of Twitter API, ...
This technical report lists all subgroups of S4, the symmetric group of degree 4. Subgroups are listed in cycle form using the integers 0, 1, 2, and 3.
This technical report lists all 4x4 matrices over GF(2). Each matrix is listed along with its order and its inverse. At the end is a summary of the number of matrices belonging to each order.
This technical report lists all 3x3 matrices over GF(2). Each matrix is listed along with its order and its inverse. At the end is a summary of the number of matrices belonging to each order.
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 ...
The general linear groups over GF(2) have an intricate and interesting structure. This report does some preliminary work in examining the structure of two of these groups by giving the conjugacy classes of 3x3 and 4x4 ...
There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 10. (There is no class 6, so the classes are ...
There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 9.
There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 8. This class includes the standard representation ...
There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 7.
There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 5.
There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 4.
There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 3.
There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 2.