# António Malheiro

## Assistant Professor, Mathematical Department

Faculdade de Ciências e Tecnologia UNL, Monte da Caparica, 2829-516 Caparica, Tel: (+351) 212948388 ext. 10832 (email)

Faculdade de Ciências e Tecnologia UNL, Monte da Caparica, 2829-516 Caparica, Tel: (+351) 212948388 ext. 10832 (email)

in

- Citation:
- Cain, A. J., R. D. Gray, and A. Malheiro. "Finite Gröbner-Shirshov bases for plactic algebras and biautomatic structures for plactic monoids." J. Algebra. 423 (2015): 37-53.

This paper shows that every Plactic algebra of finite rank admits a finite Gröbner--Shirshov basis. The result is proved by using the combinatorial properties of Young tableaux to construct a finite complete rewriting system for the corresponding Plactic monoid, which also yields the corollaries that Plactic monoids of finite rank have finite derivation type and satisfy the homological finiteness properties left and right $\mathrm{FP}_\infty$. Also, answering a question of Zelmanov, we apply this rewriting system and other techniques to show that Plactic monoids of finite rank are biautomatic.

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