Unimodular Binary Hierarchical Models
Combinatorics
2016-02-19 v2 Optimization and Control
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.
Cite
@article{arxiv.1502.06131,
title = {Unimodular Binary Hierarchical Models},
author = {Daniel Irving Bernstein and Seth Sullivant},
journal= {arXiv preprint arXiv:1502.06131},
year = {2016}
}