2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228353It 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.23 pagesCombinatoricsCommutative Algebra05E99text