- Maximal subgroups of finitely presented special inverse monoids (with M. Kambites)
Journal of the European Mathematical Society, to appear (2024).
[Preprint from arXiv]Topological finiteness properties of monoids. Part 2: special monoids, one-relator monoids, amalgamated free products, and HNN extensions (with B. Steinberg)
Documenta Mathematica, to appear (2024).
[Preprint from arXiv]On groups of units of special and one-relator inverse monoids (with N. Ruskuc)
Journal of the Institute of Mathematics of Jussieu 2023:1-44. doi:10.1017/S1474748023000439.
[Preprint from arXiv] [Final published journal version]Prefix monoids of groups and right units of special inverse monoids (with I. Dolinka)
Forum of Mathematics, Sigma Vol. 11:e97 1–19, (2023).
[Preprint from arXiv] [Final published journal version]Topological finiteness properties of monoids. Part 1: Foundations (with B. Steinberg)
Algebraic and Geometric Topology Vol. 22 (7), 3083–3170, (2022).
[Preprint from arXiv] [Final published journal version]Algorithmic properties of inverse monoids with hyperbolic and tree-like Schützenberger graphs (with P. Silva and N. Szakacs).
Journal of Algebra Vol. 611, 1 December 2022, pp. 651–687.
[Preprint from arXiv] [Final published journal version]A Lyndon's Identity theorem for one-relator monoids (with B. Steinberg)
Selecta Mathematica, New Series Vol. 28, 59 (2022).
[Preprint from arXiv] [Final published journal version]Free inverse monoids are not $\mathrm{FP}_2$ (with B. Steinberg)
Comptes Rendus Mathématique Vol. 359, issue 8 (2021), pp. 1047–1057.
[Preprint from arXiv] [Final published journal version]On equations and first-order theory of one-relator monoids (with A. Garreta)
Information and Computation Volume 281, December 2021, 104745.
[Preprint from arXiv] [Final published journal version]Ehresmann theory and partition monoids (with J. East)
Journal of Algebra Vol. 579, 2021, pp. 318–352.
[Preprint from arXiv] [Final published journal version]New results on the prefix membership problem for one-relator groups (with I. Dolinka)
Transactions of the American Mathematical Society Vol. 374, 2021, pp. 4309–4358.
[Preprint from arXiv] [Final published journal version]Undecidability of the word problem for one-relator inverse monoids via right-angled Artin subgroups of one-relator groups.
Inventiones Mathematicae Vol. 219, 2020, pp. 987–1008.
[Preprint from arXiv] [Final published journal version]- On cogrowth, amenability and the spectral radius of a random walk on a semigroup (with M. Kambites)
International Mathematics Research Notices (IMRN) Vol. 2020, No. 12, pp. 3753–3793.
- Crystal monoids and crystal bases: rewriting systems and biautomatic structures for plactic monoids of types $A_n$, $B_n$, $C_n$, $D_n$, and $G_2$ (with A. J. Cain and A. Malheiro)
Journal of Combinatorial Theory, Series A Vol. 162, 2019, pp. 406–466.
[Preprint from arXiv] [Final published journal version]- Permutation monoids and MB-homogeneity for graphs and relational structures (with T. D. H. Coleman and D. M. Evans)
European Journal of Combinatorics Vol. 78, 2019, pp. 163–189.
[Preprint from arXiv] [Final published journal version]- Universal locally finite maximally homogeneous semigroups and inverse semigroups (with I. Dolinka)
Forum Mathematicum Vol. 30(4), 2018, pp. 947–971.
[Preprint from arXiv] [Final published journal version]- On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids (with A. J. Cain and A. Malheiro)
Information and Computation Vol. 255, 2017, pp. 68–93.
[Preprint from arXiv] [Final published journal version]- Amenability and geometry of semigroups (with M. Kambites)
Transactions of the American Mathematical Society Vol. 369, 2017, pp. 8087–8103.
[Preprint from arXiv] [Final published journal version]- On regularity and the word problem for free idempotent generated semigroups (with I. Dolinka and N. Ruskuc)
Proceedings of the London Mathematical Society Vol. 114, 2017, pp. 401-432.
[Preprint from arXiv] [Final published journal version]- Diagram monoids and Graham-Houghton graphs: idempotents and generating sets of ideals (with J. East)
Journal of Combinatorial Theory, Series A Vol. 146, 2017, pp. 63-128.
[Preprint from arXiv] [Final published journal version]- Motzkin monoids and partial Brauer monoids (with I. Dolinka and J. East)
Journal of Algebra Vol. 471, 2017, pp. 251-298.
[Preprint from arXiv] [Final published journal version]- Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph (with I. Dolinka, J. D. McPhee, J. D. Mitchell, and M. Quick)
Mathematical Proceedings of the Cambridge Philosophical Society Vol. 160, 2016, pp. 437-462.
[Preprint from arXiv] [Final published journal version]- Ends of Semigroups (with S. Craik, V. Kilibarda, J. D. Mitchell, and N. Ruskuc)
Semigroup Forum Vol. 93, 2016, pp. 330-346.
[Preprint from arXiv] [Final published journal version]- Rewriting systems and biautomatic structures for Chinese, hypoplactic, and Sylvester monoids (with A. J. Cain and A. Malheiro)
International Journal of Algebra and Computation Vol. 25, 2015, no. 1-2.
[Preprint from arXiv] [Final published journal version]- Finite Gröbner-Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids (with A. J. Cain and A. Malheiro)
Journal of Algebra Vol. 423, 2015, pp. 37-53.
[Preprint from arXiv] [Final published journal version]- A strong geometric hyperbolicity property for directed graphs and monoids (with M. Kambites)
Journal of Algebra Vol. 420, 2014, pp. 373-401.
[Preprint from arXiv] [Final published journal version]- The minimal number of generators of a finite semigroup
Semigroup Forum Vol. 89, 2014, pp. 135-154.
[Preprint from arXiv] [Final published journal version]- Homotopy Bases and Finite Derivation Type for Subgroups of Monoids (with A. Malheiro)
Journal of Algebra Vol. 410, 2014, pp. 53-84.
[Preprint from arXiv] [Final published journal version]- Countable locally 2-arc-transitive bipartite graphs (with J. K. Truss)
European Journal of Combinatorics Vol. 39, 2014, pp. 122-147.
[Preprint from arXiv] [Final published journal version]- On Residual Finiteness of Monoids, their Schützenberger Groups and Associated Actions (with N. Ruskuc)
Journal of Algebra Vol. 407, 2014, pp. 21-45.
[Preprint from arXiv] [Final published journal version]- Maximal subgroups of free idempotent generated semigroups over the full linear monoid (with I. Dolinka)
Transactions of the American Mathematical Society Vol. 366, 2014, pp. 419-455.
[Preprint from arXiv] [Final published journal version]- Ideals and finiteness conditions for subsemigroups (with V. Maltcev, J. D. Mitchell and N. Ruskuc)
Glasgow Mathematical Journal Vol. 56, 2014, pp. 65-86.
[Preprint from arXiv] [Final published journal version]- Quasi-isometry and finite presentations for left cancellative monoids (with M. Kambites)
International Journal of Algebra and Computation Vol. 23, 2013, pp. 1099-1114.
[Preprint from arXiv] [Final published journal version]- Groups Acting on Semimetric Spaces and Quasi-isometries of Monoids (with M. Kambites)
Transactions of the American Mathematical Society Vol. 365, 2013, pp. 555-578.
[Preprint from arXiv] [Final published journal version]- Homotopy bases and finite derivation type for Schützenberger groups of monoids (with A. Malheiro and S. J. Pride)
Journal of Symbolic Computation Vol. 50, 2013, pp. 50-78.
[Preprint from arXiv] [Final published journal version]- Maximal subgroups of free idempotent generated semigroups over the full transformation monoid (with N. Ruskuc)
Proceedings of the London Mathematical Society Vol. 104, 2012, pp. 997-1018.
[Preprint from arXiv] [Final published journal version]- Set-homogeneous Directed Graphs (with D. Macpherson, C. Praeger and G. Royle)
Journal of Combinatorial Theory, Series B Vol. 102, 2012, pp. 474--520.
[Preprint from arXiv] [Final published journal version]- On Maximal Subgroups of Free Idempotent Generated Semigroups (with N. Ruskuc)
Israel Journal of Mathematics Vol. 189, 2012, pp. 147-176.
[Preprint from arXiv] [Final published journal version]- Green Index in Semigroups: Generators, Presentations and Automatic Structures (with A. J. Cain and N. Ruskuc)
Semigroup Forum Vol. 85, 2012, pp. 448-476.
[Preprint from arXiv] [Final published journal version]- A Svarc-Milnor Lemma for Monoids Acting by Isometric Embeddings (with M. Kambites)
International Journal of Algebra and Computation Vol. 21, 2011, pp. 1135-1147.
[Preprint from arXiv] [Final published journal version]- Presentations of Inverse Semigroups their Kernels and Extensions (with C. Carvalho and N. Ruskuc)
Journal of the Australian Mathematical Society Vol. 90, 2011, pp. 289-316.
[Final published journal version]- Homological Finiteness Properties of Monoids, their Ideals and Maximal Subgroups (with S. J. Pride)
Journal of Pure and Applied Algebra Vol. 215, 2011, pp. 3005-3024.
[Preprint from arXiv] [Final published journal version]- On properties not inherited by monoids from their Schützenberger groups (with A. Malheiro and S. J. Pride)
Information and Computation Vol. 209, 2011, pp. 1120-1134.
[Preprint from arXiv] [Final published journal version]- Generators and Relations for Subsemigroups via Boundaries in Cayley Graphs (with N. Ruskuc)
Journal of Pure and Applied Algebra Vol. 215, 2011, pp. 2761-2779.
[Final published journal version]- Locally-finite Connected-homogeneous Digraphs (with R. Moller)
Discrete Mathematics Vol. 311, 2011, pp. 1497-1517.
[Preprint from arXiv] [Final published journal version]- Finite Complete Rewriting Systems for Regular Semigroups (with A. Malheiro)
Theoretical Computer Science Vol. 412, 2011, pp. 654-661.
[Preprint from arXiv] [Final published journal version]- Countable connected-homogeneous graphs (with D. Macpherson)
Journal of Combinatorial Theory, Series B Vol. 100, 2010, pp. 97-118.[Final published journal version]- Cycle-free Partial Orders and Ends of Graphs (with J. K. Truss)
Mathematical Proceedings of the Cambridge Philosophical Society Vol. 146, 2009, pp. 535-550.
[Final published journal version]- On Residual Finiteness of Direct Products of Algebraic Systems (with N. Ruskuc)
Monatshefte fur Mathematik Vol. 158, 2009, pp. 63-69.
[Final published journal version]- k-CS-transitive Infinite Graphs
Journal of Combinatorial Theory, Series B Vol. 99, 2009, pp. 378-398.
[Final published journal version]- Green Index and Finiteness Conditions for Semigroups (with N. Ruskuc)
Journal of Algebra Vol. 320, 2008, pp. 3145-3164.
[Final published journal version]- Construction of Some Countable One-arc Transitive Bipartite Graphs (with J. K. Truss)
Discrete Mathematics Vol. 308, 2008, pp. 6392-6405.
[Final published journal version]- Construction of Some Uncountable 2-arc-transitive Bipartite Graphs (with M. Droste and J. K. Truss)
Order Vol. 25, 2008, pp. 349-357.
[Final published journal version]- Hall's Condition and Idempotent Rank of Ideals of Endomorphism Monoids
Proceedings of the Edinburgh Mathematical Society Vol. 51, 2008, pp. 1-16.
[Final published journal version]- Largest Subsemigroups of the Full Transformation Monoid (with J. D. Mitchell)
Discrete Mathematics Vol. 308, 2008, pp. 4801-4810.
[Final published journal version]- Idempotent Rank in Endomorphism Monoids of Finite Independence Algebras
Proceedings of the Royal Society of Edinburgh: Section A Mathematics Vol. 137A, 2007, pp. 303-331.
[Final published journal version]- Generating Sets of Completely 0-Simple Semigroups (with N. Ruskuc)
Communications in Algebra Vol. 33, 2005, pp. 4657-4678.
[Final published journal version]Submitted papers- Subgroups of $E$-unitary and $\mathcal{R}_1$-injective special inverse monoids (with M. Kambites)
Submitted, 27 pages.
[Preprint from arXiv]Membership problems for positive one-relator groups and one-relation monoids (with I. Foniqi and C.-F. Nyberg-Brodda)
Submitted, 32 pages.
[Preprint from arXiv]Thesis- A graph theoretic approach to combinatorial problems in semigroup theory
PhD Thesis, School of Mathematics and Statistics, University of St Andrews, 2006.
[Full thesis]