5 problems

Let $P$ be a Gorenstein polytope of dimension $d$ and degree $s$. A Gorenstein polytope is reducible with factors $F$ and $G$ if it is a Cayley join of $F$ and $G$ and … equivalent…

Let ${\boldsymbol s}=(s_1,s_2,\ldots,s_n)$ be any sequence, and let $\overleftarrow{\boldsymbol s}$ denote its reverse. Let $\mathbf{P}_n^{({\boldsymbol s})}$ be the corresponding…

Let $P$ be a Gorenstein polytope of Calabi–Yau dimension $n$, so that $E_{st}(P;u,v)$ is its stringy $E$-function. Batyrev–Nill conjecture. The following assertions hold: 1.…

Let $P$ be a Gorenstein polytope of index $r$ and dimension $d$, and let $E_{st}(P;u,v)$ denote its stringy $E$-function. Batyrev–Nill polynomiality conjecture. The function…

Let $P$ be an $n$-dimensional Gorenstein polytope of degree $d$. A polytope is a pyramid if it is the lattice pyramid over another lattice polytope. Pyramid conjecture. Every $3d$-…