Cain, Alan J., Ricardo P. Guilherme, and António Malheiro. "Quasi-crystals for arbitrary root systems and associated generalizations of the hypoplactic monoid." (Submitted).

Alan J. Cain, António Malheiro, Duarte Ribeiro. "Identities and bases in the sylvester and Baxter monoids." Journal of Algebraic Combinatorics (In Press).

Can, M.B., Casimiro Malheiro A. & A. "Idempotent Varieties of Incidence Monoids and Bipartite Posets." Algebra and Representation Theory  (2022).

A. J. Cain, M. Johnson, Kambites Malheiro M. A. "Representations and identities of plactic-like monoids." Journal of Algebra. 606 (2022): 819-850.

Cain, Alan J., António Malheiro, and Duarte Ribeiro. "Identities and bases in the hypoplactic monoid." Communications in Algebra. 50 (2022): 146-162.

Cain, A. J., and A. Malheiro. "Combinatorics of cyclic shifts in plactic, hypoplactic,  sylvester,   Baxter, and related monoids." Journal of Algebra. 535 (2019): 159-224.

Cain, Alan J., António Malheiro, and Fábio M. Silva. "Combinatorics of patience sorting monoids." Discrete Mathematics. 342.9 (2019): 2590-2611.

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.

Malheiro, António, and José Francisco Reis. "Identification of proofs via syzygies." Philosophical Transactions of the Royal Society A. 377.2140 (2019).

Cain, A. J., A. Malheiro, and F. M. Silva. "The monoids of the patience sorting algorithm." International Journal of Algebra and Computation. 29.01 (2019): 85-125.

Cain, A. J., António Malheiro, and Fábio M. Silva Conjugacy in Patience Sorting monoids., 2018.

Cain, Alan J., and António Malheiro. "Crystals and trees: Quasi-Kashiwara operators, monoids of binary trees, and Robinson?Schensted-type correspondences." Journal of Algebra. 502 (2018): 347-381.

Araújo, J., M. Kinyon, J. Konieczny, and A. Malheiro. "Decidability and Independence of Conjugacy Problems in Finitely Presented Monoids." Theoretical Computer Science. 731 (2018): 88-98.

Cain, A. J., and A. Malheiro. "Identities in plactic, hypoplactic, sylvester, Baxter, and related monoids." The Electronic Journal of Combinatorics. 25.3 (2018): P3.30 (19 pages).

Cain, Alan J., and António Malheiro. "Combinatorics of Cyclic Shifts in Plactic, Hypoplactic, Sylvester, and Related Monoids." Combinatorics on Words: 11th International Conference, WORDS 2017, Montréal, QC, Canada, September 11-15, 2017, Proceedings. Eds. Sre?ko Brlek, Francesco Dolce, Christophe Reutenauer, and Élise Vandomme. Cham: Springer International Publishing,  2017. 190-202.

Cain, A. J., and A. Malheiro. "Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson--Schensted-type correspondence for quasi-ribbon tableaux." Journal of Algebraic Combinatorics. 45.2 (2017): 475-524.

Araújo, João, Michael Kinyon, Janusz Konieczny, and António Malheiro. "Four notions of conjugacy for abstract semigroups." Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 147 (2017): 1169-1214.

Cain, A. J., G. Klein, ?. Kubat, A. Malheiro, and J. Okni?ski A note on identities in plactic monoids and monoids of upper-triangular tropical matrices. ArXiv e-prints., 2017.

Cain, A. J., R. D. Gray, and A. Malheiro. "On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids." Information and Computation. 255 (2017): 68-93.

Cain, A. J., and A. Malheiro. "Deciding conjugacy in sylvester monoids and other homogeneous monoids." Int. J. Algebra Comput.. 25 (2015): 899-915.

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.

Cain, A. J., R. D. Gray, and A. Malheiro. "Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids." Int. J. Algebra Comput.. 25 (2015): 51-80.

Araújo, J., J. Konieczny, and A. Malheiro. "Conjugation in semigroups." J. Algebra. 403 (2014): 93-134.

Gray, R. D., and A. Malheiro. "Homotopy bases and finite derivation type for subgroups of monoids." J. Algebra. 410 (2014): 53-84.

Araújo, J., M. Kinyon, and A. Malheiro. "A characterization of adequate semigroups by forbidden subsemigroups." Proc. R. Soc. Edinb., Sect. A, Math.. 143 (2013): 1115-1122.

Gray, R. D., A. Malheiro, and S. J. Pride. "Homotopy bases and finite derivation type for Schützenberger groups of monoids." J. Symb. Comput.. 50 (2013): 50-78.

Malheiro, A. "Finite derivation type for semilattices of semigroups." Semigroup Forum. 84 (2012): 515-526.

Gray, R. D., and A. Malheiro. "Finite complete rewriting systems for regular semigroups." Theor. Comput. Sci.. 412 (2011): 654-661.

Araújo, J., and A. Malheiro. "On finite complete presentations and exact decompositions of semigroups." Commun. Algebra. 39 (2011): 3866-3878.

Gray, R. D., A. Malheiro, and S. J. Pride. "On properties not inherited by monoids from their Schützenberger groups." Inf. Comput.. 209 (2011): 1120-1134.

Malheiro, A. "Finite derivation type for large ideals." Semigroup Forum. 78 (2009): 450-485.

Malheiro, A. "On Finite Semigroup Cross-Sections and Complete Rewriting Systems." International Conference on Theoretical and Mathematical Foundations of Computer Science, TMFCS-08, Orlando, Florida, USA, July 7-10, 2008. 2008. 59-63.

Malheiro, A. On trivializers and subsemigroups.. Semigroups and formal languages. Proceedings of the international conference in honour of the 65th birthday of Donald B. McAlister. Lisboa, Portugal, July 12?15, 2005.: Hackensack, NJ: World Scientific, 2007.

Malheiro, A. "Finite derivation type for Rees matrix semigroups." Theor. Comput. Sci.. 355 (2006): 274-290.

Malheiro, A. Finiteness conditions of semigroup presentations.. Eds. G. M. S. Gomes. University of Lisbon. Lisbon: University of Lisbon, 2006.

Malheiro, A. "Complete rewriting systems for codified submonoids." Int. J. Algebra Comput.. 15 (2005): 207-216.

Malheiro, A. Presentations and complete rewriting systems for semigroups. (in Portuguese). Eds. G. M. S. Gomes. Faculty of Sciences of the University of Lisbon. Lisbon: University of Lisbon, 2001.