7 citations · 15 across the 21 of their papers we have counts for
23 papers · 1 filter
Majorization and additive tuples in
Sophie Huczynska, Firdavs Rakhmonov, Chi Hoi Yip
Majorization is a fundamental tool for comparing how "spread out" the entries of two vectors are. Key majorization results were obtained for the integers by Hardy, Littlewood and P…
Cyclotomic skew partial difference sets and partial difference families
Sophie Huczynska, Tekgül Kalaycı
Skew partial difference sets (skew PDSs) are recently-introduced combinatorial objects closely related to partial difference sets (PDSs). To date, only one construction approach fo…
Graph labellings and external difference families
Gavin Angus, Sophie Huczynska, Struan McCartney
Digraph-defined external difference families were recently introduced as a natural generalization of several well-studied combinatorial objects motivated by cryptography (e.g. exte…
The Intersection Distribution: New Results and Perspectives
Sophie Huczynska, Lukas Klawuhn, Maura B. Paterson
Intersection distribution and non-hitting index are concepts introduced recently by Li and Pott as a new way to view the behaviour of a collection of finite field polynomials. With…
Digraph-defined external difference families and new circular external difference families
Sophie Huczynska, Christopher Jefferson, Struan McCartney
External difference families (EDFs) are combinatorial objects which were introduced in the early 2000s, motivated by information security applications such as the construction of A…
Strongly Regular Graphs with Generalized Denniston and Dual Generalized Denniston Parameters
Shuxing Li, James A. Davis, Sophie Huczynska +2
We construct two families of strongly regular Cayley graphs, or equivalently, partial difference sets, based on elementary abelian groups. The parameters of these two families are…
Optical orthogonal codes from a combinatorial perspective
Sophie Huczynska, Siaw-Lynn Ng
Optical orthogonal codes (OOCs) are sets of -sequences with good auto- and cross-correlation properties. They were originally introduced for use in multi-access communicatio…
Additive triples in groups of odd prime order
Sophie Huczynska, Jonathan Jedwab, Laura Johnson
Let be an odd prime. For nontrivial proper subsets of of cardinality , respectively, we count the number of additive triples, namely elemen…
New results on non-disjoint and classical strong external difference families
Sophie Huczynska, Sophie Hume
Classical strong external difference families (SEDFs) are much-studied combinatorial structures motivated by information security applications; it is conjectured that only one clas…
Denniston partial difference sets exist in the odd prime case
James A. Davis, Sophie Huczynska, Laura Johnson +1
Denniston constructed partial difference sets (PDSs) with the parameters in ele…
Non-disjoint strong external difference families can have any number of sets
Sophie Huczynska, Siaw-Lynn Ng
Strong external difference families (SEDFs) are much-studied combinatorial objects motivated by an information security application. A well-known conjecture states that only one ab…
New constructions for disjoint partial difference families and external partial difference families
S. Huczynska, L. M. Johnson
Recently, new combinatorial structures called disjoint partial difference families (DPDFs) and external partial difference families (EPDFs) were introduced, which simultaneously ge…
Internal and external partial difference families and cyclotomy
Sophie Huczynska, Laura Johnson
We introduce the concept of a disjoint partial difference family (DPDF) and an external partial difference family (EPDF), a natural generalisation of the much-studied structures of…
Strong external difference families in abelian and non-abelian groups
Sophie Huczynska, Christopher Jefferson, Silvia Nepsinska
Strong external difference families (SEDFs) have applications to cryptography and are rich combinatorial structures in their own right; until now, all SEDFs have been in abelian gr…
Characterising bimodal collections of sets in finite groups
Sophie Huczynska, Maura B. Paterson
A collection of disjoint subsets of a finite abelian group is said to have the \emph{bimodal} property if, for any non-zero group element , eit…
Weighted external difference families and R-optimal AMD codes
Sophie Huczynska, Maura B. Paterson
In this paper, we provide a mathematical framework for characterizing AMD codes that are R-optimal. We introduce a new combinatorial object, the reciprocally-weighted external diff…
Existence and Non-Existence Results for Strong External Difference Families
Sophie Huczynska, Maura B. Paterson
We consider strong external difference families (SEDFs); these are external difference families satisfying additional conditions on the patterns of external diferences that occur,…
On well quasi-order of graph classes under homomorphic image orderings
N. Ruskuc, Sophie Huczynska
In this paper we consider the question of well quasi-order for classes defined by a single obstruction within the classes of all graphs, digraphs and tournaments, under the homomor…
Beyond sum-free sets in the natural numbers
Sophie Huczynska
For an interval [1,N] in the natural numbers, investigating subsets S of [1,N] such that |{(x,y) in S^2:x+y in S}|=0, known as sum-free sets, has attracted considerable attention.…
Simple permutations and algebraic generating functions
Robert Brignall, Sophie Huczynska, Vincent Vatter
A simple permutation is one that does not map a nontrivial interval onto an interval. It was recently proved by Albert and Atkinson that a permutation class with only finitely simp…
Decomposing simple permutations, with enumerative consequences
Robert Brignall, Sophie Huczynska, Vince Vatter
We prove that every sufficiently long simple permutation contains two long almost disjoint simple subsequences. This result has applications to the enumeration of restricted permut…
Grid classes and the Fibonacci dichotomy for restricted permutations
Sophie Huczynska, Vincent Vatter
We introduce and characterise grid classes, which are natural generalisations of other well-studied permutation classes. This characterisation allows us to give a new, short proof…
Frequency permutation arrays
Sophie Huczynska, Gary L. Mullen
Motivated by recent interest in permutation arrays, we introduce and investigate the more general concept of frequency permutation arrays (FPAs). An FPA of length n=m lambda and di…