Tomas Nilson
Universitetslektor|Senior Lecturer
- Professional title: Senior Lecturer
- Academic title: Doctor of Philosophy (PhD)
- Other title: Retired
- Email: tomas.nilson@miun.se
- Room number: F309
- Location: Sundsvall
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- Employed at the subject:
- Mathematics
Area of interest
Discrete mathematics with emphasis on design theory. Applications include, among other areas, experimental design.
"It may not be a coincidence that the two systems in the universe that most impress us with their open-ended complex design –life and mind – are based on discrete combinatorial systems".
Steven Pinker, The Language Instinct, Penguin, London, 1994.
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.
Other information
Publications
Articles in journals
Doctoral theses, comprehensive summaries
Manuscripts
Reports
Articles in journals
Nilson, T. (2022). Intercalates in double and triple arrays. Journal of combinatorial designs (Print), vol. 30: 3, pp. 135-151.
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
Nilson, T. (2013). Some matters of great balance. Dis. (Comprehensive summary) Sundsvall : Mid Sweden University, 2013 (Mid Sweden University doctoral thesis : 144)
Manuscripts
Nilson, T. & Schiebold, C. On the noncommutative two-dimensional Toda lattice.
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).