6 problems

Generic maximal-rank conjecture. The combinatorial hypersimplices of nonnegative rank $2n$ form a dense open subset of $\mathcal{R}_{n,k}$.

Let $P_1$ and $P_2$ be polytopes. Their nonnegative rank is the smallest number of nonnegative factors in a nonnegative factorization of a slack matrix of the polytope. Product add…

Let $S_n$ be the slack matrix of any $n$-gon, and let $\lfloor x\rfloor$ denote the largest integer not exceeding $x$. Polygon slack-matrix upper-bound conjecture. … and equality h…

Let $A$ be a nonnegative matrix, let $A\otimes A$ denote its Kronecker square, and write $\operatorname{rank}(A)$ for its ordinary rank. Self-Kronecker-product conjecture. … The so…

For a nonnegative matrix $M$, its nonnegative rank $\operatorname{rank}_+(M)$ is the least inner dimension of a factorization of $M$ into two nonnegative matrices. The ordinary ran…

Let $M$ be a random linear Euclidean distance matrix of dimension $n$, so that $M$ is an $n\times n$ matrix of pairwise squared distances generated by randomly chosen points on a l…