A finiteness theorem for Markov bases of hierarchical models

Details A finiteness theorem for Markov bases of hierarchical models A finiteness theorem for Markov bases of hierarchical models

2004-01-27

arxiv.org/abs/math/0401379v2

Mathematics

Combinatorics

13 pages, 1 figure

Scientific paper

We show that the complexity of the Markov bases of multidimensional tables stabilizes eventually if a single table dimension is allowed to vary. In particular, if this table dimension is beyond a computable bound, the Markov bases consist of elements of Markov bases of smaller tables. We give an explicit formula for this bound in terms of Graver bases. We also compute these Markov and Graver complexities for all $K \times 2 \times 2 \times 2 $ tables.

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