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

Employed at the subject:

Mathematics

Department:

Department of Engineering, Mathematics and Science Education (IMD)

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

Personal home page

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).