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arXiv · 0708.2312

Markov bases for two-way subtable sum problems

Hisayuki Hara·Akimichi Takemura·Ruriko Yoshida
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Abstract

It has been well-known that for two-way contingency tables with fixed row sums and column sums the set of square-free moves of degree two forms a Markov basis. However when we impose an additional constraint that the sum of a subtable is also fixed, then these moves do not necessarily form a Markov basis. Thus, in this paper, we show a necessary and sufficient condition on a subtable so that the set of square-free moves of degree two forms a Markov basis.

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Hisayuki Hara, Akimichi Takemura, Ruriko Yoshida. 2007-08-17. Markov bases for two-way subtable sum problems. https://doi.org/10.1016/j.jpaa.2008.11.019

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