6 problems

Let $\Pi$ be a projective plane of order $q$, let $U$ be a rank-$3$ residue zero-pattern model satisfying the identity-pattern minor constraints, and let $T_U$ denote its tangent s…

Let $q\geq 3$, let $\Pi$ be a projective plane of order $q$, and consider a $4\times4$ determinant initial form of its combinatorial incidence matrix. A degenerate diamond is a con…

Let $G$ be a partial geometry with parameters $(s,t,\alpha)$ as in the paper, where $d=2^i\ge 2$ and $d'=2^j\ge 2$, and let $\mathcal{P}$ be a projective plane of order $q=2^{i+j}$…

Throughout, let $q$ be an odd prime power, let $V=\mathbb{F}_{q}^{3}$ be equipped with a non-degenerate symmetric bilinear form, and let $Q$ be its corresponding quadratic form. Wr…

The 2-rank conjecture. The $2$-ranks satisfy the following:

Keith's conjecture.