2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130545The set of all m-tuples of compatible full conditional distributions on discrete random variables is an algebraic set whose defining ideal is a unimodular toric ideal. We identify the defining polynomials of these ideals with closed walks on a bipartite graph. Our algebraic characterization provides a natural generalization of the requirement that compatible conditionals have identical odds ratios and holds regardless of the patterns of zeros in the conditional arrays.15 pagesAlgebraic GeometryCombinatoricsStatistics Theorytext