António Malheiro
Full Professor, Mathematics Department
Faculdade de Ciências e Tecnologia UNL, Monte da Caparica, 2829-516 Caparica, Tel: (+351) 212948388 ext. 10832 (email)
Crystal monoids & crystal bases: Rewriting systems and biautomatic structures for plactic monoids of types An, Bn, Cn, Dn, and G2
- Citation:
- Cain, A. J., R. D. Gray, and A. Malheiro. "Crystal monoids & crystal bases: Rewriting systems and biautomatic structures for plactic monoids of types An, Bn, Cn, Dn, and G2." Journal of Combinatorial Theory, Series A. 162 (2019): 406-466.
Abstract:
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's crystal bases and analogies of Young tableaux, and on Lecouvey'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.
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