Tomas Nilson
Universitetslektor|Senior Lecturer
- Professional title: Senior Lecturer
- Academic title: Doctor of Philosophy (PhD)
- Other title: Head of Department
- Department: Department of Mathematics and Science Education (MOD)
- Telephone: 010-142 85 22
- Email: tomas.nilson@miun.se
- Room number: E305
- Subject: Mathematics
Area of interest
Discrete mathematics with emphasis on design theory. Applications include, among other areas, experimental design.
Current research
Ongoing projects are aimed primarily at proving existence, finding construction methods and investigating properties for different types of row-column designs. As for future goals, a proof of Agrawal’s conjecture for the optimal designs called triple arrays is high on the list. This problem has been open for more than 50 years, but recently we got a partial result when we managed to prove the existence of an infinite family.
In addition, we now start a project where mathematical physics and combinatorics work together. The principal aim of this project is to develop a deeper understanding of the interface between integrable systems and cellular automata.
Teaching and tutoring
Assistent supervisor for PhD-student Kristoffer Karlsson.
Other information
Programme co-ordinator for the foundation year.
Publications
Articles in journals
Doctoral theses, comprehensive summaries
Reports
Articles in journals
Nilson, T. & Schiebold, C. (2020). Solution formulas for the two-dimensional Toda lattice and particle-like solutions with unexpected asymptotic behaviour. Journal of Nonlinear Mathematical Physics, vol. 27: 1, pp. 57-94.
Bailey, R. A. , Cameron, P. J. & Nilson, T. (2018). Sesqui-arrays, a generalisation of triple arrays. The Australasian Journal of Combinatorics, vol. 71: 3, pp. 427-451.
Nilson, T. & Cameron, P. J. (2017). Triple arrays from difference sets. Journal of combinatorial designs (Print), vol. 25: 11, pp. 494-506.
Nilson, T. & Öhman, L. (2015). Triple arrays and Youden squares. Designs, Codes and Cryptography, vol. 75: 3, pp. 429-451.
Nilson, T. & Heidtmann, P. (2014). Inner balance of symmetric designs. Designs, Codes and Cryptography, vol. 71: 2, pp. 247-260.
Nilson, T. (2011). Pseudo-Youden designs balanced for intersection. Journal of Statistical Planning and Inference, vol. 141: 6, pp. 2030-2034.
Doctoral theses, comprehensive summaries
Nilson, T. (2013). Some matters of great balance. Dis. (Comprehensive summary) Sundsvall : Mid Sweden University, 2013 (Mid Sweden University doctoral thesis : 144)
Reports
Nilson, T. & Schiebold, C. (2018). Solution formulas for the two-dimensional Toda lattice and particle-like solutions with unexpected asymptotic behaviour. (Mid Sweden Mathematical Reports 2).