Principal ideals in a plactic monoid always intersect
arXiv:2410.11047
Abstract
This note presents a proof that two principal ideals in a plactic monoid always intersect. Namely, this means that the plactic monoids are both left and right reversible. To the author's knowledge, this result has not yet appeared in the literature studying this monoid. This result holds for both finite rank plactic monoids and the infinite rank plactic monoid.
Results unchanged, but the argument has been restructured for the sake of clarity. Removed discussion of left ideals intersecting with right ideals, as this is trivially true in any monoid. Added slightly more discussion of involution monoids