Gröbner bases for staged trees

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 Gröbner basis whose intial terms are squarefree. The proof of this result is based on Sullivant's toric fiber product construction.

17 pages, 3 figures

References in corpus (3)

• On the toric algebra of graphical models
• Sequential importance sampling for multiway tables
• Equations defining probability tree models

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