| Automaton semigroups AJ Cain Theoretical Computer Science 410 (47-49), 5022-5038, 2009 | 54 | 2009 |
| Finite Gröbner–Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids AJ Cain, RD Gray, A Malheiro Journal of Algebra 423, 37-53, 2015 | 50 | 2015 |
| Nine Chapters on the Semigroup Art AJ Cain https://archive.org/details/cain_semigroups_a4_screen, 2012 | 26* | 2012 |
| Presentations for subsemigroups of groups AJ Cain PQDT-Global, 2005 | 24 | 2005 |
| A note on identities in plactic monoids and monoids of upper-triangular tropical matrices AJ Cain, G Klein, Ł Kubat, A Malheiro, J Okniński arXiv preprint arXiv:1705.04596, 2017 | 21 | 2017 |
| Visual thinking and simplicity of proof AJ Cain Philosophical Transactions of the Royal Society A 377 (2140), 20180032, 2019 | 20 | 2019 |
| Identities in plactic, hypoplactic, sylvester, Baxter, and related monoids AJ Cain, A Malheiro arXiv preprint arXiv:1611.04151, 2016 | 20 | 2016 |
| Crystal monoids & crystal bases: rewriting systems and biautomatic structures for plactic monoids of types An, Bn, Cn, Dn, and G2 AJ Cain, RD Gray, A Malheiro Journal of Combinatorial Theory, Series A 162, 406-466, 2019 | 19 | 2019 |
| Automaton semigroups: new constructions results and examples of non-automaton semigroups T Brough, AJ Cain Theoretical Computer Science 674, 1-15, 2017 | 19 | 2017 |
| Context-free rewriting systems and word-hyperbolic structures with uniqueness AJ Cain, V Maltcev International Journal of Algebra and Computation 22 (07), 1250061, 2012 | 19 | 2012 |
| Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids AJ Cain, RD Gray, A Malheiro International Journal of Algebra and Computation 25 (01n02), 51-80, 2015 | 18 | 2015 |
| Automaton semigroup constructions T Brough, AJ Cain Semigroup Forum 90, 763-774, 2015 | 16 | 2015 |
| Deus ex Machina and the Aesthetics of Proof. AJ Cain Mathematical Intelligencer 32 (3), 2010 | 16 | 2010 |
| Representations and identities of plactic-like monoids AJ Cain, M Johnson, M Kambites, A Malheiro Journal of Algebra 606, 819-850, 2022 | 13 | 2022 |
| Identities and bases in the hypoplactic monoid AJ Cain, A Malheiro, D Ribeiro Communications in Algebra 50 (1), 146-162, 2022 | 13 | 2022 |
| Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson–Schensted–Knuth-type correspondence for quasi-ribbon tableaux AJ Cain, A Malheiro Journal of Algebraic Combinatorics 45 (2), 475-524, 2017 | 13 | 2017 |
| Green index in semigroups: generators, presentations, and automatic structures AJ Cain, R Gray, N Ruškuc Semigroup Forum 85, 448-476, 2012 | 12 | 2012 |
| Subsemigroups of groups: presentations, Malcev presentations, and automatic structures AJ Cain, EF Robertson, N Ruškuc Walter de Gruyter 9 (3), 397-426, 2006 | 12 | 2006 |
| Automatic presentations for semigroups AJ Cain, G Oliver, N Ruškuc, RM Thomas Information and Computation 207 (11), 1156-1168, 2009 | 11 | 2009 |
| Deciding conjugacy in sylvester monoids and other homogeneous monoids AJ Cain, A Malheiro International Journal of Algebra and Computation 25 (05), 899-915, 2015 | 10 | 2015 |