3 problems

Corank-three four-neighbor conjecture. Every vertex in the state polytope of $I_A$ has at most four neighbors.

State-polytope valency conjecture. The maximum valency of a vertex in the state polytope of $I_A$ is bounded above by a function depending only on the corank of $A$.

Let $n$ and $l$ be positive integers, and let … For the polytope $P(\ell)$, write $f_k$ for the number of its faces of dimension $k$. Delannoy face-number conjecture. The state pol…