The unimodular triangulation conjecture for lecture hall polytopes

Let $\boldsymbol{s}=(s_1,\ldots,s_d)$ be an integer sequence, and let $P_d^{(\boldsymbol{s})}$ denote the lecture hall polytope associated to $\boldsymbol{s}$. A triangulation is unimodular if every simplex in it has normalized volume one. The unimodular triangulation conjecture. For any $\boldsymbol{s}=(s_1,\ldots,s_d)$, $P_d^{(\boldsymbol{s})}$ admits a unimodular triangulation.

This conjecture is presented alongside the conjecture that all lecture hall polytopes have the integer decomposition property. The concluding remarks indicate that these properties are known in important families, but that full characterizations for arbitrary integer sequences remain open.