9 problems

For each sequence $s$, let the $s$-permutahedron be the generalized permutahedral object defined in the source. A polytopal subdivision is a subdivision whose cells are polytopes.…

Weeping Willow Conjecture. Any component of $\mathcal{F}(n)$ outside the polytopal closure stems from the polytopal closure of $\mathcal{F}(m)$ for some $m>n$, via 4--1 vertex-remo…

Klee–Nevo–Novik–Zheng's conjecture. There exists a unique polytopal complex ${\mathcal C}$ in ${\mathbb R}^d$ such that: (i) one face of ${\mathcal C}$ is the cross-polytope…

The polytopal cellulation conjecture. There exists a unique polytopal complex $\mathcal C$ in $\mathbb R^d$ such that: (i) one face of $\mathcal C$ is the cross-polytope…

The regularity conjecture. If $\mathcal{P}$ is central and complete, then

Let $M_1$ and $M_2$ be orientable manifolds of dimensions $n_1$ and $n_2$, possibly with boundaries, with $n_1+n_2=n$, PL embedded in general position in $\mathbb{R}^n$. Let $X$ be…

Let $\mathcal{P}\subset\mathbb{R}^2$ be a hereditary polytopal complex, and let $F$ be the maximum length of the boundary of a polytope in $\mathcal{P}$. Regularity conjecture. … T…

Let $\mathcal{P}\subset\mathbb{R}^2$ be a hereditary polytopal complex, and let $F$ be the maximum length of the boundary of a polytope in $\mathcal{P}$. Regularity conjecture. … T…

Let $P$ and $Q$ be two cubes, and let $f:V(P)\rightarrow V(Q)$. A cubical map is a map between the corresponding cubical face complexes that sends each cube into a cube. Cubical ap…