Identities of the plactic monoid
Łukasz Kubat, Jan Okniński · Semigroup Forum · 2014
It is shown that the plactic monoid M of rank $$3$$ satisfies the identity $$wvvwvw=wvwvvw$$ where $$v=xyyx xy xyyx$$ and $$w= xyyx yx xyyx$$ . This is accomplished by first showing that certain simple monoids related to $$M$$ satisfy this identity. These simple monoids are natural generalizations of the bicyclic monoid $$B$$ , which satisfies the identity $$w=v$$ by a result of Adjan.