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arXiv · 2410.11047

Principal ideals in a plactic monoid always intersect

Daniel Turaev
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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.

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Daniel Turaev. 2024-10-14. Principal ideals in a plactic monoid always intersect. https://arxiv.org/abs/2410.11047

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