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The Markov Bases Database

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Notes

  1. N is the number of random variables for those models where the state space is a product space.
  2. dim is the dimension of the model. dim+1 is the rank of the sufficient statistics matrix.
  3. d is the cardinality of the state space.
  4. The properties in the table are:
    • binary: binary variables
    • hierarchical: is it hierarchical
    • graph: is it a graph-model
    • graphical: is it a graphical (clique) model
    • normal: is the semigroup normal
    • unique: is the Markov Basis unique
    • reducible: is the model reducible; that is, does the simplicial complex have a complete separator?
  5. deg is the Markov degree, the highest degree of an element in any minimial Markov basis.
  6. The size of a minimal Markov basis.
  7. The number of symmetry classes (usually the maximal symmetry).
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properties size and complexity output
binary
hierarchical
graph
graphical
normal
unique
reducible
N
dimension
state space card.
Markov degree
minimal size
symmetry classes
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Notes

  1. The fields 'name', 'description' and 'comments' are searched for the given string. Use '*' and '?' as wildcard symbols. The search is case insensitive. Note that this field is ignored if the checkbox is not checked!
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page last update on November 15 2020. ->Contact