The IDP 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 lattice polytope is integer decomposition property (IDP) if every lattice point in each positive integer dilation is a sum of lattice points of the original polytope. The IDP conjecture. For any $\boldsymbol{s}=(s_1,\ldots,s_d)$, $P_d^{(\boldsymbol{s})}$ is IDP.

The authors report computational evidence for many randomly generated sequences and no examples of non-IDP lecture hall polytopes. A dilation identity for these polytopes suggests that arguments known for monotone sequences might extend to arbitrary integer sequences, but the full characterization remains open.