5 problems

Let $S\in\{0,1\}^{m\times n}$. A matrix is a slack matrix if it is the slack matrix of a polytope. Polynomial-time recognition conjecture. There is an algorithm polynomial in $m,n$…

Let $\ell(d)$ and $s(d)$ respectively denote the numbers of combinatorially distinct $2$-level polytopes and $2$-level suspensions in dimension $d$. Suspension conjecture for 2-lev…

Let $\ell(d)$ be the number of combinatorially distinct $2$-level polytopes in dimension $d$. Enumeration conjecture for 2-level polytopes. The number $\ell(d)$ of combinatorially…

Let $P$ be a $2$-level $d$-polytope, and let $f_0(P)$ and $f_{d-1}(P)$ denote its numbers of vertices and facets, respectively. Vertex-facet product conjecture. For every $2$-level…

Vertex/facet trade-off conjecture. One has