Gröbner Bases for Toric Staged Trees

Staged tree models are a generalisation of discrete graphical models coding conditional independence statements between events represented in a tree graph. Their algebraic properties were studied by Duarte and Görgen in their recent paper "Equations Defining Probability Tree Models". In this talk we aim to explain the combinatorics involved in obtaining the defining equations for such models. In the toric case we show that the generators of the toric ideal are a quadratic Gröbner basis. We connect our study with the theory of toric fiber products as introduced by Sullivant in 2006. This is joint work with Eliana Duarte.