Unimodular hierarchical models and their Graver bases
Abstract
Given a simplicial complex whose vertices are labeled with positive integers, one can associate a vector configuration whose corresponding toric variety is the Zariski closure of a hierarchical model. We classify all the vertex-weighted simplicial complexes that give rise to unimodular vector configurations. We also provide a combinatorial characterization of their Graver bases.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2017
- DOI:
- 10.48550/arXiv.1704.09018
- arXiv:
- arXiv:1704.09018
- Bibcode:
- 2017arXiv170409018B
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Optimization and Control
- E-Print:
- Minor changes from previous version. This version to appear in Journal of Algebraic Statistics