4 problems

Two-dimensionality conjecture. No new simple symplectic triple systems appear in characteristic different from $3$, and every simple symplectic triple system in characteristic $3$…

Let an NWBTS$(v;b)$ denote the nearly well-balanced triple system studied in the paper, equivalently an optimal data placement for triple replication with $v$ servers and $b$ block…

Let $\mathrm{TS}(v,\lambda)$ be a $2$-$(v,3,\lambda)$ triple system, and let a zero-sum $3$-flow be a map from its blocks to $\{\pm1,\pm2\}$ such that the sum of the assigned value…

Quasigroup formulation of the Brown–Erdős–Sós conjecture. For every $c>0$, there is a threshold $n_0$ such that if $Q$ has order $n\geq n_0$, then for every such subset $S$, whenev…