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Gröbner bases for
staged trees
Lamprini Ananiadi and Eliana Duarte |
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Vol. 12 (2021), No. 1, 1–20
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Abstract |
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We consider the problem of finding generators of the toric ideal associated to a combinatorial object called a staged tree. Our motivation to consider this problem originates from the use of staged trees to represent discrete statistical models such as conditional independence models and discrete Bayesian networks. The main theorem in this article states that toric ideals of staged trees that are balanced and stratified are generated by a quadratic Gröbner basis whose initial ideal is square-free. We apply this theorem to construct Gröbner bases of a subclass of discrete statistical models represented by staged trees. The proof of the main result is based on Sullivant’s toric fiber product construction (J. Algebra 316:2 (2007), 560–577). |
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Keywords
graphical model, toric ideals, staged tree, Markov bases,
toric fiber product
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Mathematical Subject Classification 2010
Primary: 13P10, 13P25
Secondary: 14M25, 05E40, 68W30
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Milestones
Received: 7 October 2019
Revised: 21 December 2020
Accepted: 5 January 2021
Published: 9 April 2021
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Authors |
| Lamprini Ananiadi | |
| Otto-Von-Guericke Universität Magdeburg Germany |
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| Eliana Duarte | |
| Otto-Von-Guericke Universität Magdeburg Germany |
Max-Planck-Institute for Mathematics
in the Sciences Leipzig Germany |
