Representations and identities of involution Plactic-like monoids arising from the meet of the stalactic congruence and its dual

Bin Bin Han, Wen Ting Zhang, Yan Feng Luo

Let ${\mathsf{mSt}}_n$ be the plactic-like monoid obtained by factoring the free monoid over a finite alphabet ${\mathcal{A}}_n$ by the meet of the stalactic congruence and its dual. I…