5 problems

Kubat–Okniński's conjecture. Every plactic monoid of finite rank satisfies a non-trivial semigroup identity.

Let $\mathbb{T}$ denote the tropical semifield, let $UT_2(\mathbb{T})$ be the monoid of all $2\times 2$ upper triangular matrices over $\mathbb{T}$, and let $\mathcal{B}$ be the bi…

Finite-rank plactic identity conjecture. For each $n \geq 4$, there is a non-trivial identity satisfied by ${\mathsf{plac}}_n$.

For each positive integer $n$, let $M_n(\mathbb T)$ be the monoid of $n\times n$ tropical matrices. The source notes that polynomial growth alone does not force a semigroup identit…

For each positive integer $n$, let $M_n(\mathbb T)$ be the monoid of $n\times n$ tropical matrices. A nontrivial semigroup identity is an identity between distinct semigroup words…