5 problems

Let $\mathcal T$ be a staged tree with non-toric $V(\ker \varphi_{\mathcal T})$ that uses color set $S$. Let $\mathcal T'$ be a staged tree such that its restriction to color set…

A staged tree model is a statistical model associated with a staged tree, and it has toric structure when its defining algebra can be represented as a toric algebra. The toric-stru…

Let $\mathcal{T}$ be a balanced staged tree, and let $\ker\varphi_\mathcal{T}$ denote its toric ideal. Duarte–Görgen's conjecture. The ideal $\ker\varphi_\mathcal{T}$ has a Gröbner…

Let a staged tree be regular when, for every pair of vertices in the same stage and every pair of outgoing edges, the corresponding subtree monomials satisfy the required equality…

Maximal-path ideal conjecture. The kernel of $\varphi$ is exactly the ideal generated by maximal paths,