Tomas Nilson

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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.


Articles in journals

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)  


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).