4 problems

Let $\mathbb{P}_n$ denote the plactic monoid on rank $n$, and let a tropical representation of $\mathbb{P}_n$ be faithful when it distinguishes all elements of $\mathbb{P}_n$. The…

Let $A$ be a finite ordered set, let $\Bbbk$ be a commutative unital ring, and let $\mathbf{Pl}_A$ denote the plactic monoid on $A$. Theorem gives an injective algebra map from the…

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

Let $a,b$ be the parameters defining the relevant Kazhdan–Lusztig cells, let $r\geq 1$, and let signed permutations lie in $B_n$. Two signed permutations are $r$-cycle equivalent (…