@article {CGM15,
	title = {Crystal monoids \& crystal bases: Rewriting systems and biautomatic structures for plactic monoids of types An, Bn, Cn, Dn, and G2},
	journal = {Journal of Combinatorial Theory, Series A},
	volume = {162},
	year = {2019},
	note = {<p>Submitted</p>
},
	pages = {406-466},
	abstract = {<p>This paper constructs presentations via finite complete rewriting systems for plactic monoids of types $A_n$, $B_n$, $C_n$, $D_n$, and $G_2$, using a unified proof strategy that depends on Kashiwara{\textquoteright}s crystal bases and analogies of Young tableaux, and on Lecouvey{\textquoteright}s presentations for these monoids. As corollaries, we deduce that plactic monoids of these types have finite derivation type and satisfy the homological finiteness properties left and right $\mathrm{FP}_\infty$. These rewriting systems are then applied to show that plactic monoids of these types are biautomatic.</p>
},
	url = {https://doi.org/10.1016/j.jcta.2018.11.010},
	author = {Cain, A.J. and R.D. {Gray} and Malheiro, A.}
}
