5 problems

Oda's conjectures. The following two statements are true: (1) every smooth polytope has the IDP; and (2) if $P,Q\subset\mathbb{R}^n$ are smooth polytopes and the normal fan of $P$…

SNP conjecture. For $t\in\mathbb Z_{>0}$, we have

Let $\mathfrak{S}_3$ denote the symmetric group on three letters, let $\Pi\subseteq\mathfrak{S}_3$, and let $B_n(\Pi)$ be the associated polytope. A conjecture on the integer decom…

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 i…

Long-edge conjecture. Simple lattice polytopes with sufficiently long edges have the integer decomposition property, where the required meaning of “sufficiently long” is given by a…