All publications

Presentations for Subsemigroups of Groups
Ph.D. thesis, University of St Andrews, St Andrews, 2005.
Subsemigroups of virtually free groups: finite Malcev presentations and testing for freeness
[with E. F. Robertson & N. Ruškuc]
Mathematical Proceedings of the Cambridge Philosophical Society, 141, no. 1 (2006), pp. 57–66.
DOI: 10.1017/s0305004106009236. MR: 2238642. ZBL: 1115.20043.
Subsemigroups of groups: presentations, Malcev presentations, and automatic structures
[with E. F. Robertson & N. Ruškuc]
Journal of Group Theory, 9, no. 3 (2006), pp. 397–426.
DOI: 10.1515/jgt.2006.027. MR: 2226621. ZBL: 1151.20044.
A group-embeddable non-automatic semigroup whose universal group is automatic
Glasgow Mathematical Journal, 48, no. 2 (2006), pp. 337–342.
DOI: 10.1017/s0017089506003107. MR: 2256982. ZBL: 1108.20056.
Cancellativity is undecidable for automatic semigroups
Quarterly Journal of Mathematics, 57, no. 3 (2006), pp. 285–295.
DOI: 10.1093/qmath/hai023. MR: 2253587. ZBL: 1126.20039.
A note on “Cancellativity is undecidable for automatic semigroups”
Unpublished note, 2006.
Malcev presentations for subsemigroups of groups — a survey
In C. M. Campbell, M. Quick, E. F. Robertson, & G. C. Smith, eds, Groups St Andrews 2005 (Vol. 1), no. 339 in London Mathematical Society Lecture Note Series, pp. 256–268 (Cambridge: Cambridge University Press, 2007).
DOI: 10.1017/CBO9780511721212.018. MR: 2328165.
Cancellative and Malcev presentations for finite Rees index subsemigroups and extensions
[with E. F. Robertson & N. Ruškuc]
Journal of the Australian Mathematical Society, 84, no. 1 (2008), pp. 39–61.
DOI: 10.1017/s1446788708000086. MR: 2469266. ZBL: 1156.20048.
Automatic presentations for cancellative semigroups
[with G. Oliver, N. Ruškuc & R. M. Thomas]
In C. Martín-Vide, H. Fernau, & F. Otto, eds, Language and Automata Theory and Applications: Second International Conference, Tarragona, Spain, March 13–19, 2008, no. 5196 in Lecture Notes in Computer Science, pp. 149–159 (Springer, 2008).
DOI: 10.1007/978-3-540-88282-4_15. MR: 2540320. ZBL: 1157.20332.
Malcev presentations for subsemigroups of direct products of coherent groups
Journal of Pure and Applied Algebra, 213, no. 6 (2009), pp. 977–990.
DOI: 10.1016/j.jpaa.2008.10.006. MR: 2498789. ZBL: 1178.20050.
Automaton semigroups
Theoretical Computer Science, 410, no. 47–49 (2009), pp. 5022–5038.
DOI: 10.1016/j.tcs.2009.07.054. MR: 2583696. ZBL: 1194.68133.
Automatic presentations for semigroups
[with G. Oliver, N. Ruškuc & R. M. Thomas]
Information and Computation, 207, no. 11 (2009), pp. 1156–1168.
DOI: 10.1016/j.ic.2009.02.005. MR: 2566948. ZBL: 1192.20040.
Decision problems for finitely presented and one-relation semigroups and monoids
[with V. Maltcev]
International Journal of Algebra and Computation, 19, no. 6 (2009), pp. 747–770.
DOI: 10.1142/s0218196709005366. MR: 2572873. ZBL: 1201.20055.
Monoids presented by rewriting systems and automatic structures for their submonoids
International Journal of Algebra and Computation, 19, no. 6 (2009), pp. 771–790.
DOI: 10.1142/s0218196709005317. MR: 2572874. ZBL: 1201.20054.
Automatic semigroups and Bruck–Reilly extensions
Acta Mathematica Hungarica, 126, no. 1–2 (2010), pp. 1–15.
DOI: 10.1007/s10474-009-8063-8. MR: 2593314. ZBL: 1259.20061.
Automatic presentations and semigroup constructions
[with G. Oliver, N. Ruškuc & R. M. Thomas]
Theory of Computing Systems, 47, no. 2 (2010), pp. 568–592.
DOI: 10.1007/s00224-009-9216-4. MR: 2652030. ZBL: 1204.68118.
Deus ex machina and the aesthetics of proof
Mathematical Intelligencer, 32, no. 3 (September 2010), pp. 7–11.
DOI: 10.1007/s00283-010-9141-z. MR: 2721302. ZBL: 1247.00009.
An annotated translation of Yves Marie André’s Essay on Beauty (1741)
(Ebook, 2010).
Unary FA-presentable semigroups
[with N. Ruškuc & R. M. Thomas]
International Journal of Algebra and Computation, 22, no. 4 (2012).
DOI: 10.1142/S0218196712500385. MR: 2946303. ZBL: 1285.03048.
Green index in semigroup theory: generators, presentations, and automatic structures
[with R. Gray & N. Ruškuc]
Semigroup Forum, 85, no. 3 (2012), pp. 448–476.
DOI: 10.1007/s00233-012-9406-2. MR: 3001595. ZBL: 1270.20059.
Context-free rewriting systems and word-hyperbolic structures with uniqueness
[with V. Maltcev]
International Journal of Algebra and Computation, 22, no. 7 (2012).
DOI: 10.1142/S0218196712500610. MR: 2999367. ZBL: 1284.68320.
Nine Chapters on the Semigroup Art
(Lecture notes, 2012).
Monoids $\mathrm{Mon}\langle a,b \mid a^\alpha b^\beta a^\gamma b^\delta = b\rangle$ admit finite complete rewriting systems
[with V. Maltcev]
Technical report. Febuary 2013.
arXiv: 1302.0982.
Monoids $\mathrm{Mon}\langle a,b \mid a^\alpha b^\beta a^\gamma b^\delta a^\varepsilon b^\phi = b\rangle$ admit finite complete rewriting systems
[with V. Maltcev]
Technical report. Febuary 2013.
arXiv: 1302.2819.
Unary FA-presentable binary relations: transitivity and classification results
[with N. Ruškuc]
Technical report. March 2013.
arXiv: 1303.0214.
For a few elements more: A survey of finite Rees index
[with V. Maltcev]
Technical report. July 2013.
arXiv: 1307.8259.
Hyperbolicity of monoids presented by confluent monadic rewriting systems
Beiträge zur Algebra und Geometrie, 54, no. 2 (October 2013), pp. 593–608.
DOI: 10.1007/s13366-012-0116-4. MR: 3095744. ZBL: 1326.20056.
Automatic structures for subsemigroups of Baumslag–Solitar semigroups
Semigroup Forum, 87, no. 3 (2013), pp. 537–552.
DOI: 10.1007/s00233-013-9490-y. MR: 3128706. ZBL: 1326.20057.
Finitely presented monoids with linear Dehn function need not have regular cross-sections
[with V. Maltcev]
Semigroup Forum, 88, no. 2 (2014), pp. 300–315.
DOI: 10.1007/s00233-013-9531-6. MR: 3189098. ZBL: 1300.20057.
Markov semigroups, monoids, and groups
[with V. Maltcev]
International Journal of Algebra and Computation, 24, no. 5 (August 2014).
DOI: 10.1142/S021819671450026X. MR: 3254716. ZBL: 1325.20055.
Subalgebras of FA-presentable algebras
[with N. Ruškuc]
Algebra Universalis, 72, no. 2 (October 2014), pp. 101–123.
DOI: 10.1007/s00012-014-0293-0. MR: 3257650. ZBL: 1321.08001.
Hopfian and co-hopfian subsemigroups and extensions
[with V. Maltcev]
Demonstratio Mathematica, 47, no. 4 (2014), pp. 791–804.
DOI: 10.2478/dema-2014-0064. MR: 3290386. ZBL: 1312.20051.
Finite Gröbner–Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids
[with R. D. Gray & A. Malheiro]
Journal of Algebra, 423 (Febuary 2015), pp. 37–53.
DOI: 10.1016/j.jalgebra.2014.09.037. MR: 3283708. ZBL: 1311.20055.
A simple non-bisimple congruence-free finitely presented monoid
[with V. Maltcev]
Semigroup Forum, 90, no. 1 (Febuary 2015), pp. 184–188.
DOI: 10.1007/s00233-014-9607-y. MR: 3297818. ZBL: 1317.20049.
Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids
[with R. D. Gray & A. Malheiro]
International Journal of Algebra and Computation, 25, no. 1-2 (2015).
DOI: 10.1142/S0218196715400044. MR: 3325877. ZBL: 1326.20058.
Automaton semigroup constructions
[with T. Brough]
Semigroup Forum, 90, no. 3 (June 2015), pp. 763–774.
DOI: 10.1007/s00233-014-9632-x. MR: 3345953. ZBL: 1336.20062.
Deciding conjugacy in sylvester monoids and other homogeneous monoids
[with A. Malheiro]
International Journal of Algebra and Computation, 25, no. 5 (August 2015).
DOI: 10.1142/S0218196715500241. MR: 3384086. ZBL: 06481131.
A countable family of congruence-free finitely presented monoids
[with F. Al-Kharousi, V. Maltcev & A. Umar]
Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum, 81, no. 3–4 (2015), pp. 437–445.
DOI: 10.14232/actasm-013-028-z. MR: 3443762. ZBL: 1363.20044.
Decision problems for word-hyperbolic semigroups
[with M. Pfeiffer]
Journal of Algebra, 465 (November 2016), pp. 287–321.
DOI: 10.1016/j.jalgebra.2016.07.007. MR: 3537824. ZBL: 06621117.
Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson–Schensted–Knuth-type correspondence for quasi-ribbon tableaux
[with A. Malheiro]
Journal of Algebraic Combinatorics, 45, no. 2 (March 2017), pp. 475–524.
DOI: 10.1007/s10801-016-0714-6. MR: 3604065. ZBL: 1359.05135.
Growths of endomorphisms of finitely generated semigroups
[with V. Maltcev]
Journal of the Australian Mathematical Society, 102, no. 2 (April 2017), pp. 163–184.
DOI: 10.1017/S1446788716000264. MR: 3621637. ZBL: 06714329.
Automaton semigroups: new constructions results and examples of non-automaton semigroups
[with T. Brough]
Theoretical Computer Science, 674 (2017), pp. 1–15.
DOI: 10.1016/j.tcs.2017.02.003. MR: 3634703. ZBL: 06715025.
On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids
[with R. D. Gray & A. Malheiro]
Information and Computation, 255, no. 1 (August 2017), pp. 68–93.
DOI: 10.1016/j.ic.2017.05.003.
Combinatorics of cyclic shifts in plactic, hypoplactic, sylvester, and related monoids
[with A. Malheiro]
In S. Brlek, F. Dolce, C. Reutenauer, & É. Vandomme, eds, Combinatorics on Words: 11th International Conference, Montréal, Canada, September 11–15, 2017, vol. 10432 of Lecture Notes in Computer Science, pp. 190–202 (Springer, 2017).
DOI: 10.1007/978-3-319-66396-8_18.

Forthcoming

Submitted

Crystal monoids & crystal bases: rewriting systems and biautomatic structures for plactic monoids of types ${A}_n$, ${B}_n$, ${C}_n$, ${D}_n$, and ${G}_2$
[with R. D. Gray & A. Malheiro]
Submitted.
arXiv: 1412.7040.
Identities in plactic, hypoplactic, sylvester, Baxter, and related monoids
[with A. Malheiro]
Submitted.
arXiv: 1611.04151.
Crystals & trees: quasi-Kashiwara operators, monoids of binary trees, and Robinson–Schensted-type correspondences
[with A. Malheiro]
Submitted.
arXiv: 1702.02998.
A note on identities in plactic monoids and monoids of upper-triangular tropical matrices
[with G. Klein, Ł. Kubat, A. Malheiro & J. Okniński]
Submitted.
arXiv: 1705.04596.
The monoids of the patience sorting algorithm
[with A. Malheiro & F. Silva]
Submitted.
arXiv: 1706.06884.
Combinatorics of cyclic shifts in plactic, hypoplactic, sylvester, Baxter, and related monoids
[with A. Malheiro]
Submitted.
arXiv: 1709.03974.