2 problems

Let $\mathcal{L}_d$ be the set of bracelet matrices of dimension $d$. A monoid is a set closed under matrix multiplication and containing an identity element $\mathbb{I}_d$. Monoid…

Let $t\in \mathbb{N}$ be arbitrary. Write $K^{\infty}_t$ for the finite min-plus semiring with entries drawn from $\{0,\ldots,t,\infty\}$, and let $M_3(K^{\infty}_t)$ denote the mo…