Now showing items 41-60 of 74

  • Why is Symmetry So Hard? 

    Maurer (2011-05-13)
    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 ...
  • Extending Symmetric Variable-Pair Transitivities Using State-Space Transformations 

    Maurer, Peter (2011-05-13)
    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 ...
  • Bootstrapping Bipartite Graphs Consisting of Edges Based on Ontology Terms Occurring in Scientific Abstract 

    Morillo, Daniel (2011-05-13)
    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 ...
  • MovieOracle System 

    Yao, Yao (2011-09-13)
    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, ...
  • Anti-Symmetry and Logic Simulation 

    Maurer, Peter M. (2012-01-19)
    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 Group of GF(2)^3 

    Maurer, Peter M. (2012-01-19)
    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.
  • The Subgroups of S4 in Cycle Form 

    Maurer, Peter M. (2012-01-19)
    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.
  • The Subgroups of S3 in Cycle Form 

    Maurer, Peter M. (2012-01-19)
    This technical report lists all subgroups of S3 in cycle form.
  • The General Linear Group of GF(2)^4 

    Maurer, Peter M. (2012-01-19)
    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.
  • The Subgroups of S6 in Cycle Form 

    Maurer, Peter M. (2012-01-19)
    This technical report lists all subgroups of S6 in cycle form using the integers 0-5.
  • The Subgroups of S5 in Cycle Form 

    Maurer, Peter M. (2012-01-19)
    This technical report lists all subgroups of S5 in cycle form, using the integers 0-4.
  • Primitive Polynomials for the Field GF(3): Degree 2 through Degree 11 

    Maurer, Peter M. (2013-09-20)
    This report lists the primitive polynomials over GF(3) of degree 2 through 11. These polynomials were generated using a new matrix-based technique I invented.
  • The Class 1 4x4 Faithful Representations of S4 over GF(2) 

    Maurer, Peter M. (2013-09-20)
    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 1.
  • Primitive Polynomials for the Field GF(2): Degree 2 through Degree 16 

    Maurer, Peter M. (2013-09-20)
    This report lists the primitive polynomials over GF(2) of degree 2 through 16. These polynomials were generated using a new matrix-based technique I invented.
  • The Class 2 4x4 Faithful Representations of S4 over GF(2) 

    Maurer, Peter M. (2013-09-20)
    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.
  • The Number of Conjugates of the Standard Representation of Sn in the General Linear Group over GF(2) 

    Maurer, Peter M. (2013-09-20)
    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 ...
  • The Representations of GF(8) in GL3(2) 

    Maurer, Peter M. (2013-09-20)
    As is well known (or should be well known) the finite field GF(2^k) can be represented in the general linear group of kxk matrices over GF(2). There are many such representations. This report gives the 8 representations ...
  • The Representations of GF(8) in GL3(2) 

    Maurer, Peter M. (2013-09-20)
    This report gives one subgroup of each of the conjugacy classes of the subgroups of S7.
  • The Class 5 4x4 Faithful Representations of S4 over GF(2) 

    Maurer, Peter M. (2013-09-20)
    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.
  • The Class 4 4x4 Faithful Representations of S4 over GF(2) 

    Maurer, Peter M. (2013-09-20)
    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.