Papers/Preprints

"Optical orthogonal codes from a combinatorial perspective", S.Huczynska and S-L. Ng, ArXiV preprint arXiv:2411.06955. "Beyond uniform cyclotomy", S. Huczynska, L. Johnson and M. B. Paterson, ArXiV preprint arXiv:2406.16805 "Additive triples in groups of odd prime order", S.Huczynska, J. Jedwab and L. Johnson, ArXiV preprint arXiv:2405.04638 "New results on non-disjoint and classical strong external difference families", S. Huczynska and S. Hume, ArXiV preprint arXiv:2403.16284 "Denniston partial difference sets exist in the odd prime case", J. A. Davis, S. Huczynska, L. Johnson and J. Polhill, Finite Fields and their Applications, Volume 99, October 2024, 102499 "Non-disjoint strong external difference families can have any number of sets", S. Huczynska and S-L. Ng, Archiv der Mathematik 122 (2024), p. 609–619. "Decomposing complete graphs into isomorphic complete multipartite graphs", S. Huczynska and M. B. Paterson, New Advances in Designs, Codes and Cryptography, Fields Institute Communications, ed C.J. Colbourn and J. H. Dinitz, Springer, 2024. "New constructions for disjoint partial difference families and external partial difference families", S. Huczynska and L. Johnson, Journal of Combinatorial Designs 32 (2024), p. 190-213. "Internal and external partial difference families and cyclotomy", S.Huczynska and L. Johnson, Discrete Mathematics 346 (2023), no. 3, Paper No. 113295, 24 pp. "Strong external difference families in abelian and non-abelian groups ", S.Huczynska, C. Jefferson and S. Nepsinska, Cryptography and Communications 13 (2021) p.331–341. "Characterising bimodal collections of sets in finite groups", S.Huczynska and M.B. Paterson, Archiv der Mathematik 113 (2019), p.571–580. "Weighted external difference families and R-optimal AMD codes", S.Huczynska and M.B. Paterson, Discrete Mathematics 342, 3 (2019), p.855-867. "Existence and non-existence results for strong external difference families", S.Huczynska and M.B. Paterson, Discrete Mathematics. 341, 1 (2018) p. 87-95 "Near-complete external difference families", J.A. Davis, S. Huczynska, and G.L. Mullen, Designs, Codes and Cryptography. 84, 3, p. 415-424 (2017) 10 p. "On well quasi-order of graph classes under homomorphic image orderings", S.Huczynska and N. Ruskuc, European Journal of Combinatorics. 63, p. 164-175 (2017) 12 p. "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. "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 .

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.

Conference Papers

• "Modelling Equidistant Frequency Permutation Arrays: An Application of Constraints to Mathematics", Huczynska, S., McKay, P., Miguel, I. J. & Nightingale, P. W., 2009, Proceedings of the 15th International Conference on Principles and Practice of Constraint Programming. Gent, I. (ed.). Springer, Vol. 5732. p. 50-64 15 p. (Lecture Notes in Computer Science).

• "Modelling Equidistant Frequency Permutation Arrays in Constraints", Gent, I. P., McKay, P., Miguel, I., Nightingale, P. & Huczynska, S., 2009, Eighth Symposium on Abstraction, Reformulation, and Approximation,: SARA 2009, Lake Arrowhead, California, USA, 8-10 August 2009. Bulitko, V. & Beck, C. J. (eds.). AAAI Press

Books

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

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