Dr. Sophie Huczynska
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.
- Session 2016-7: I am on sabbatical during Semester 1, and will be teaching the module "Rings and Fields" in Semester 2.
Current research interests
- Finite fields
Various aspects of finite fields, especially the existence and properties of generating elements with extra properties.
A range of topics in combinatorics: some related to my interests in finite fields (eg construction of combinatorial objects and codes using finite fields) and others of quite a different flavour (ranging from the structure theory of classes of combinatorial objects, to permutation patterns, to intersecting sets, and many more).
Recent/ forthcoming events
- I am a member of the Local Organizing Committee of the 2018 British Mathematical Colloquium, which will be held in St Andrews in June 2018.
- I was a member of the Organizing Committee of Fq12 - the 12th International Conference on Finite Fields and their Applications, which was held in summer 2015 at Saratoga Springs NY.
- I was a Plenary Speaker at Fq11 - the 11th International Conference on Finite Fields and their Applications, which took place in Magdeburg, Germany, in July 2013. Information about the conference may be found here .
- I was an Invited Speaker at the RICAM Workshop on Finite Fields and their Applications: Character sums and polynomials, September 2012, Austria.
- To read a non-specialist account of my work and its possible applications, see the article "Euler's Revolution" by Ian Stewart, which appeared in the New Scientist magazine (issue 24-30 March 2007).
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.
"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.
"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 .
"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
- I referee for various journals including Designs, Codes and Cryptography, Discrete Applied Mathematics, Finite Fields and their Applications, IEEE Transactions on Information Theory and others.
- I am a reviewer for Zentralblatt MATH..
- I was Local Organizer of the 22nd British Combinatorial Conference, held here in St Andrews in July 2009. The webpage from the conference is available here.
- I was on the organizing committee of several in the series of "International Conferences on Pattern Avoiding Permutations".
School of Mathematics and Statistics
University of St Andrews
Mathematical Institute (Room 214)
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.