3 problems

Non-word-representability conjecture. All simplified de Bruijn graphs $S(n,k)$ are non-word-representable for $n\geq 4$ and $k\geq 3$.

Let $\mathcal{E}(q,k,\ell)$ denote the maximum number of eBugs in an $\ell$-valid colouring with $q$ colours and $k$ LEDs per eBug. An optimal colouring is one attaining the upper…

Rational generating-function conjecture. If $D$ is a fixed odd prime number, then this exponential generating function is the ratio of two polynomials, each of degree $D-1$. For…