4 problems

Let $Erdahl(n)$ denote the space used in the paper, and for $f\in Erdahl(n)$ let $proj(f)=g$, where $(g,h)$ is the unique extremal pair associated with $f$. Continuity conjecture f…

For each $n\geq 6$, let $LD_n$ be the lattice defined in Dutour (2005), and let a covering maximum be a lattice whose covering density decreases under perturbation. The covering-de…

Face-number conjecture. For every $d$-dimensional perfect prismatoid $P$, there exists a $d$-dimensional lattice Delaunay polytope $Q$ such that

Let $P$ and $P_1$ be perfect Delaunay polytopes for $\mathbb{Z}^n$ and call them adjacent when the quadratic rank of their common vertex set is $2$. An adjacency component is a col…