Gröbner bases for staged trees

Lamprini Ananiadi and Eliana Maria Duarte Gelvez

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Submission date: 09. Oct. 2019
Pages: 19
Bibtex
MSC-Numbers: 113P1
Keywords and phrases: graphical models, toric ideals, Markov Bases
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Abstract:
In this article we consider the problem of finding generators of the toric ideal associated to a combinatorial object called a staged tree. Our main theorem states that toric ideals of staged trees that are balanced and stratified are generated by a quadratic Gro ̈bner basis whose initial ideal is squarefree. The proof of this result is based on Sullivant’s toric fiber product construction.