Dr. Sophie Huczynska

Current Position

I am a Senior Lecturer in Pure Mathematics at the School of Mathematics and Statistics at the University of St Andrews. Until October 2010, I was a Royal Society Dorothy Hodgkin Research Fellow . My research is mainly in the areas of combinatorics and finite fields; I also have interests in algebra and theoretical computer science. I am a member of the Centre for Interdisciplinary Research in Computational Algebra (CIRCA).

Please note: I work on a part-time basis. Currently, I can be contacted in the department on Mondays, and until mid-afternoon on other days.

News: Scottish Combinatorics Meeting 2017 will be held in St Andrews on 24th and 25th April, organised by Nik Ruškuc and myself.


Current research interests

Recent/ forthcoming events

Academic service

Public understanding


  • Fiona Brunk:(2009) completed her PhD on "Intersection problems in combinatorics", jointly supervised by Nik Ruskuc and myself.
  • I was second supervisor for Anna Schroeder, who completed her PhD under the primary supervision of Colva Roney-Dougal.



  • "Surveys in Combinatorics", 2009, S.Huczynska, J.D.Mitchell and C.Roney-Dougal (eds). LMS Lecture Note Series, 365, Cambridge University Press 2009.

    Book chapters

  • "Existence results for finite field polynomials with specified properties", in Finite Fields and Their Applications: Character Sums and Polynomials, P. Charpin, A. Pott and A. Winterhof (eds), De Gruyter, Berlin, Boston, 2013.
  • "Well quasi-order in combinatorics: embeddings and homomorphisms", S.Huczynska and N. Ruskuc, Surveys in combinatorics 2015, 261--293, London Math. Soc. Lecture Note Ser., 424, Cambridge Univ. Press, Cambridge, 2015.

    Journal papers

  • "Existence and non-existence results for strong external difference families", S. Huczynska and M.B. Paterson, submitted (available on ArXiv).
  • "On well quasi-order of graph classes under homomorphic image orderings", S. Huczynska and N. Ruskuc, submitted (available on ArXiv).
  • "Near-complete external difference families", J.A.Davis, S. Huczynska and G.L.Mullen, Des. Codes Cryptogr. (2016).
  • "Homomorphic image orders on combinatorial structures", S.Huczynska and N.Ruskuc, Order 32 (2015), 205--226.
  • "Beyond sum-free sets in the natural numbers", S. Huczynska, The Electronic Journal of Combinatorics, Volume 21, Issue 1 (2014), P1.21
  • "Existence and properties of k-normal elements over finite fields", S. Huczynska, G.L. Mullen, D. Panario and D. Thomson, Finite Fields and Their Applications 124 (2013), 170--183.
  • "The strong primitive normal basis theorem", S.D. Cohen and S. Huczynska, Acta Arithmetica 143 (2010), 299--332.
  • "Some Erdo"s-Ko-Rado theorems for injections", F. Brunk and S. Huczynska, European Journal of Combinatorics 31 (2010), 839--860.
  • "Equidistant frequency permutation arrays and related constant composition codes", S. Huczynska, Designs, Codes and Cryptography 54 (2010), 109--120.
  • "The extent to which subsets are additively closed", S. Huczynska, G.L. Mullen and J. Yucas, Journal of Combinatorial Theory, Series A, 116 (2009), 831--843.
  • "Decomposing simple permutations, with enumerative consequences", R. Brignall, S. Huczynska and V. Vatter, Combinatorica 28 (2008), 385--400.
  • "Simple permutations and algebraic generating functions", R. Brignall, S. Huczynska and V. Vatter, Journal of Combinatorial Theory, Series A, 115, 423--441.
  • "Pattern classes of permutations via bijections between linearly ordered sets", S. Huczynska and N. Ruskuc, European Journal of Combinatorics 29 (2008), 118--139.
  • "Powerline communication and the 36 officers problem", S. Huczynska, Phil. Trans. R. Soc. A, 364 (2006).
  • "Frequency permutation arrays", S. Huczynska and G.L. Mullen, Journal of Combinatorial Designs 14 (2006), 463--478.
  • "Grid classes and the Fibonacci dichotomy for restricted permutations", S. Huczynska and V. Vatter, The Electronic Journal of Combinatorics 13 (2006)
  • "Primitive free cubics with specified norm and trace", S. Huczynska and S.D. Cohen, Transactions of the American Mathematical Society 355 (2003), 3099--3116.
  • "Primitive free quartics with specified norm and trace", S.D. Cohen and S. Huczynska, Acta Arithmetica 109 (2003), 359--385.
  • "The Primitive Normal Basis Theorem- without a computer", S.D. Cohen and S. Huczynska, Journal of the London Mathematical Society, 67 (2003), 41--56 .

    Conference papers

  • "Modelling equidistant frequency permutation arrays in constraints", Ian P. Gent, Paul McKay, Ian Miguel, Pete Nightingale and Sophie Huczynska, Proceedings of Principles and Practice of Constraint Programming(CP 2009).
  • "The Homer System", S. Colton and S. Huczynska, Automated Deduction � CADE-19: 19th International Conference on Automated Deduction, 2003, Franz Baeder (ed), Lecture Notes in Computer Science, Springer.

    Other work-related activities

    Contact details:

    Sophie Huczynska
    School of Mathematics and Statistics
    University of St Andrews
    Mathematical Institute (Room 214)
    North Haugh
    St Andrews, Fife, KY16 9SS

    Tel: +44 (0)1334 463711
    E-mail: My email address is: sh70 'at' st-andrews.ac.uk
    I am also contactable at: sophie.huczynska 'at' st-andrews.ac.uk.