Normal Binary Hierarchical Models

TL;DR

This paper investigates the normality and compressed properties of vector configurations derived from simplicial complexes, providing classifications and operations that preserve these properties for complexes with up to six vertices.

Contribution

It offers a comprehensive analysis of normal and compressed vector configurations from simplicial complexes, including classifications and operations that preserve these properties.

Findings

Classified all normal complexes on up to six vertices.

Classified all compressed complexes on up to six vertices.

Identified operations preserving normality in simplicial complexes.

Abstract

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 of the normal complexes on up to six vertices. We repeat this analysis for compressed vector configurations, classifying all of the compressed complexes on up to six vertices.