@article {2017arXiv170504596C,
	title = {A note on identities in plactic monoids and monoids of upper-triangular tropical matrices},
	journal = {ArXiv e-prints},
	year = {2017},
	note = {<p>n/a</p>
},
	abstract = {<p> This paper uses the combinatorics of Young tableaux to prove the plactic monoid of infinite rank does not satisfy a non-trivial identity, by showing that the plactic monoid of rank n cannot satisfy a non-trivial identity of length less than or equal to n. A new identity is then proven to hold for the monoid of n{\texttimes}n upper-triangular tropical matrices. Finally, a straightforward embedding is exhibited of the plactic monoid of rank 3 into the direct product of two copies of the monoid of 3{\texttimes}3 upper-triangular tropical matrices, giving a new proof that the plactic monoid of rank 3 satisfies a non-trivial identity. </p>
},
	keywords = {05E99 (Primary), 14T05, 16Y60 (Secondary), 20M30, Mathematics - Combinatorics, Mathematics - Group Theory},
	url = {https://arxiv.org/abs/1705.04596},
	author = {Cain, A.J. and Klein, G. and Kubat, {\L}. and Malheiro, A. and Okni{\'n}ski, J.}
}
