Markov bases for two-way subtable sum problems

Details Markov bases for two-way subtable sum problems Markov bases for two-way subtable sum problems

2007-08-17

arxiv.org/abs/0708.2312v1

Journal of Pure and Applied Algebra, Vol.213, Issue 8, 1507-1521. (2009)

Mathematics

Combinatorics

23 pages

Scientific paper

10.1016/j.jpaa.2008.11.019

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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