Automaton semigroups AJ Cain Theoretical Computer Science 410 (47-49), 5022-5038, 2009 | 46 | 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 | 37 | 2015 |

Presentations for subsemigroups of groups AJ Cain PQDT-Global, 2005 | 23 | 2005 |

Context-free rewriting systems and word-hyperbolic structures with uniqueness AJ Cain, V Maltcev International Journal of Algebra and Computation 22 (07), 1250061, 2012 | 17 | 2012 |

Automaton semigroup constructions T Brough, AJ Cain Semigroup Forum 90 (3), 763-774, 2015 | 16 | 2015 |

Automaton semigroups: new constructions results and examples of non-automaton semigroups T Brough, AJ Cain Theoretical Computer Science 674, 1-15, 2017 | 15 | 2017 |

Identities in plactic, hypoplactic, sylvester, Baxter, and related monoids AJ Cain, A Malheiro arXiv preprint arXiv:1611.04151, 2016 | 14 | 2016 |

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 | 14 | 2015 |

Deus ex Machina and the Aesthetics of Proof AJ Cain The Mathematical Intelligencer 32 (3), 7-11, 2010 | 13 | 2010 |

Nine Chapters on the Semigroup Art. AJC Porto & Lisbon, 2020 AJ Cain | 13 | |

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 | 12 | 2019 |

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 | 12 | 2017 |

Green index in semigroups: generators, presentations, and automatic structures AJ Cain, R Gray, N Ruškuc Semigroup Forum 85 (3), 448-476, 2012 | 11 | 2012 |

Automatic presentations for semigroups AJ Cain, G Oliver, N Ruškuc, RM Thomas Information and Computation 207 (11), 1156-1168, 2009 | 11 | 2009 |

Subsemigroups of groups: presentations, Malcev presentations, and automatic structures AJ Cain, EF Robertson, N Ruškuc Walter de Gruyter 9 (3), 397-426, 2006 | 11 | 2006 |

Decision problems for finitely presented and one-relation semigroups and monoids AJ Cain, V Maltcev International Journal of Algebra and Computation 19 (06), 747-770, 2009 | 10 | 2009 |

Subsemigroups of virtually free groups: finite Malcev presentations and testing for freeness AJ Cain, EF Robertson, N Ruškuc Mathematical Proceedings of the Cambridge Philosophical Society 141 (1), 57-66, 2006 | 10 | 2006 |

Deciding conjugacy in sylvester monoids and other homogeneous monoids AJ Cain, A Malheiro International Journal of Algebra and Computation 25 (05), 899-915, 2015 | 9 | 2015 |

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 | 8 | 2017 |

Hyperbolicity of monoids presented by confluent monadic rewriting systems AJ Cain Beiträge zur Algebra und Geometrie/Contributions to Algebra and Geometry 54 …, 2013 | 8 | 2013 |