10 problems

TP-to-TN obstruction conjecture. All TP obstructions contain a TN obstruction.

TN-obstruction finiteness conjecture. For every $k$, there are finitely many $k$-variable TN obstructions.

Bounded variability conjecture. All patterns have bounded variability.

TP-obstruction growth conjecture. There are infinitely many TP obstructions, and the number of TP obstructions with a given number of rows grows quickly, perhaps exponentially, wit…

Inhibiting-set atom bound conjecture. Every inhibiting set of a non-completable partial matrix with variability $k$ contains at most $k+1$ atoms.

Unbounded variability conjecture. The variability of non-completable patterns is unbounded.

TN-to-TP completion conjecture. All TN-completable patterns are also TP-completable.

Let $E_m$ be the $m\times m$ $(0,-1)$-matrix with $-1$s in positions $(2,m),(3,m-1),\ldots,(m,2)$, and let $F_m$ be the $m\times m$ $(0,-1)$-matrix with $-1$s in positions…

Let $A \in \mathbb{C}^{n\times n}$ and $\tilde{A}\in \mathbb{C}^{(n+1)\times (n+1)}$ with $n \geq 4$ be the matrices defined by … Here $\operatorname{nd}$ is the normal defect and…

Let $A \in \mathbb{C}^{n\times n}$ and $\tilde{A}\in \mathbb{C}^{(n+1)\times (n+1)}$ with $n \geq 4$ be the matrices defined by … Here $\operatorname{nd}$ denotes the normal defect…