The Markov Bases Database


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  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).


properties size and complexity output
state space card.
Markov degree
minimal size
symmetry classes
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  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!
  2. You can collect a list of models in the text area. If the checkbox before the name list is checked, then only entries whose name matches one of the lines are shown. In order to select a list of models, you can use the following steps:
    1. Select the models by selecting the checkboxes which appear in the database.
    2. Click on the "Select" button on top of the page. This inserts all selected models into the list.
    3. Make sure that the checkbox before the list is checked and click on the "Submit Query" button at the bottom of the search form.
    4. If the checkbox is not checked you can go to the next page or do a different search. The list will be saved but not applied, so you can add further entries to the list.
    Wildcards ('*' and '?') can be used in the list.
  3. Note that, if any criterion (other than 'ignore') is given for some property, then only those entries of the database are considered where this property is known (and recorded in the database). Thus in this case, any entry where this property is not known is not shown at all, regardless of the criterion.

page last update on November 15 2020. ->Contact