Dr. Sophie Huczynska

Current Position

I am a 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 number theory and combinatorics; I also have interests in algebra and theoretical computer science. I am a member of the Centre for Interdiscipinary Research in Computational Algebra (CIRCA).

Please note: I am now working on a part-time basis. I can be contacted in the department on Tuesdays, Wednesdays and Fridays.

Brief career history

Ph.D. (2002): Department of Mathematics, University of Glasgow. Supervisors: Bob Odoni, Steve Cohen. Thesis title: "Primitive free elements of Galois fields".

Research Associate (2003): Centre for Intelligent Systems and their Applications (CISA), School of Informatics, University of Edinburgh.

Teaching Fellow in Pure Mathematics (2003-4): School of Mathematics and Statistics, University of St Andrews.

Royal Society Dorothy Hodgkin Research Fellow (2004-10): School of Mathematics and Statistics, University of St Andrews.

Lecturer in Pure Mathematics (2010-present): School of Mathematics and Statistics, University of St Andrews.

Teaching

Session 2011-12, Semester 2: I am teaching the Linear Algebra part of MT2001. Lecture notes and tutorial sheets are available via the MMS system.

Current research interests

Finite fields I am interested in many aspects of finite fields, especially the existence and properties of primitive, free elements with extra properties.
Combinatorial designs I have an interest in the construction and properties of a range of combinatorial objects and designs, in particular those constructible using finite fields.
Combinatorics of permutations One of my main interests at present may be broadly described as "combinatorics of permutations". I'm interested in all sorts of topics related to this, including:
- Permutation arrays are appealing combinatorial objects, which arise from coding with permutations and recently been applied to powerline communications (the technology which enables data to be transmitted through the electric power grid).
- Permutation patterns When permutations are considered under the pattern containment order, the resulting area of combinatorics is not only interesting in its own right, but has a natural connection with sorting machines, familiar from theoretical computer science.
- Intersection problems for sets of permutations Many interesting questions may be asked about intersecting sets of permutations (and similar objects), in particular about maximum size and structure.
Research-related responsibilities
- I am a member of the British Combinatorial Committee .
Public understanding
- 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).
Supervision

Fiona Brunk:(2009) completed her PhD on "Intersection problems in combinatorics", jointly supervised by Nik Ruskuc and myself.

Publications

To appear/submitted

"Existence results for finite field polynomials with specified properties", invited survey article for RICAM workshop September 2012, de Gruyter, to appear.

"Existence and properties of k-normal elements over finite fields", S.Huczynska, G.L.Mullen, D.Panario and D.Thomson, preprint.

"Beyond sum-free sets in the natural numbers", S. Huczynska, preprint.

Published

Books

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

Journal papers

"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

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 the Third International Conference on Pattern Avoiding Permutations (Florida, March 2005) and the Fourth International Conference on Pattern Avoiding Permutations (Iceland, June 2006).

Contact details:

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

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