Unimodular Binary Hierarchical Models

TL;DR

This paper classifies simplicial complexes that produce unimodular binary hierarchical models, providing a construction and characterization via excluded minors, and showing closure under Alexander duality.

Contribution

It offers a complete classification and construction method for unimodular binary hierarchical models based on simplicial complexes, including a new characterization using excluded minors.

Findings

Classifies simplicial complexes yielding unimodular models

Provides a construction method for all such models

Shows closure under Alexander duality

Abstract

Associated to each simplicial complex is a binary hierarchical model. We classify the simplicial complexes that yield unimodular binary hierarchical models. Our main theorem provides both a construction of all unimodular binary hierarchical models, together with a characterization in terms of excluded minors, where our definition of a minor allows the taking of links and induced complexes. A key tool in the proof is the lemma that the class of unimodular binary hierarchical models is closed under the Alexander duality operation on simplicial complexes.