Normal Binary Hierarchical Models

Each simplicial complex and integer vector yields a vector configuration whose combinatorial properties are important for the analysis of contingency tables. We study the normality of these vector configurations including a description of operations on simplicial complexes that preserve normality, constructions of families of minimally nonnormal complexes, and computations classifying all but six of the normal complexes on up to six vertices. We repeat this analysis for compressed vector configurations, classifying all but six of the compressed complexes on up to six vertices.