Prof Nik Ruskuc
Director of Research
Professor
- Phone
- +44 (0)1334 46 3787
- nik.ruskuc@st-andrews.ac.uk
- Office
- 303 MI
- Location
- Mathematical Institute
Research areas
Combinatorial semigroup theory: generating sets for semigroups and defining semigroups by presentations (generators and defining relations); presentations for substructures and algebraic constructions;
Subsemigroups: index and rank;
Group and semigroup presentations;
Transformation semigroups: properties of finite and infinite semigroups of mappings from a set into itself;
Machine and languages (theoretical computer science) in algebra: automatic structures, decidability;
Combinatorics of permutations, words, etc: pattern classes, decidability questions in combinatorics;
Computational algebra: algorithms and packages for computing with algebraic structures.
PhD supervision
- Theodor Thorbjornsen
- Zhongyi Zhou
- Jung Won Cho
- Victoria Ironmonger
- Callum Barber
- Yayi Zhu
- Jiaping Lu
Selected publications
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A characterisation of semigroups with only countably many subdirect products with Z
Clayton, A. M. W., Reilly, C. & Ruskuc, N., 1 Jun 2024, (Accepted/In press) In: Bulletin of the Australian Mathematical Society.Research output: Contribution to journal › Article › peer-review
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Open access
Congruences of maximum regular subsemigroups of variants of finite full transformation semigroups
Dolinka, I., East, J. & Ruskuc, N., 15 Jan 2025, In: Journal of Algebra. 662, p. 431-464Research output: Contribution to journal › Article › peer-review
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Open access
Decidability of well quasi-order and atomicity for equivalence relations under embedding orderings
Ironmonger, V. L. & Ruskuc, N., 14 Feb 2024, (E-pub ahead of print) In: Order. 26 p.Research output: Contribution to journal › Article › peer-review
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Open access
Graph products of residually finite monoids are residually finite
Cho, J. W., Gould, V., Ruskuc, N. & Yang, D., 15 Jan 2025, In: Journal of Algebra. 662, p. 514-527Research output: Contribution to journal › Article › peer-review
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On finite presentability of subsemigroups of the monogenic free inverse semigroup
Cho, J. W. & Ruskuc, N., 14 Oct 2024, (Accepted/In press) In: Glasgow Mathematical Journal.Research output: Contribution to journal › Article › peer-review
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Open access
On the diameter of semigroups of transformations and partitions
East, J., Gould, V., Miller, C., Quinn-Gregson, T. & Ruskuc, N., Jul 2024, In: Journal of the London Mathematical Society. 110, 1, 34 p., e12944.Research output: Contribution to journal › Article › peer-review
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Open access
On groups of units of special and one-relator inverse monoids
Gray, R. D. & Ruskuc, N., 21 Nov 2023, (E-pub ahead of print) In: Journal of the Institute of Mathematics of Jussieu. FirstView, 44 p.Research output: Contribution to journal › Article › peer-review
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Open access
On minimal ideals in pseudo-finite semigroups
Gould, V., Miller, C., Quinn-Gregson, T. & Ruskuc, N., 1 Dec 2023, In: Canadian Journal of Mathematics. 75, 6, p. 2007-2037 31 p.Research output: Contribution to journal › Article › peer-review
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Open access
On the number of countable subdirect powers of unary algebras
Ruskuc, N. & De Witt, B. L., 1 Sept 2023, In: International Journal of Algebra and Computation. 33, 06, p. 1183-1194 12 p.Research output: Contribution to journal › Article › peer-review
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Open access
On separability finiteness conditions in semigroups
Miller, C., O'Reilly, G., Quick, M. & Ruskuc, N., Dec 2022, In: Journal of the Australian Mathematical Society. 113, 3, p. 402-430Research output: Contribution to journal › Article › peer-review