Now showing items 1-8 of 8

    • Beyond sum-free sets in the natural numbers 

      Huczynska, Sophie (2014-02-07) - Journal article
      For an interval [1,N]⊆N, sets S⊆[1,N] with the property that |{(x,y)∈S2:x+y∈S}|=0, known as sum-free sets, have attracted considerable attention. In this paper, we generalize this notion by considering r(S)=|{(x,y)∈S2:x+y∈S}|, ...
    • Existence and non-existence results for strong external difference families 

      Huczynska, Sophie; Paterson, Maura B. (2018-01) - Journal article
      We consider strong external difference families (SEDFs); these are external difference families satisfying additional conditions on the patterns of external differences that occur, and were first defined in the context of ...
    • Homomorphic image orders on combinatorial structures 

      Huczynska, Sophie; Ruskuc, Nik (2015-07) - Journal article
      Combinatorial structures have been considered under various orders, including substructure order and homomorphism order. In this paper, we investigate the homomorphic image order, corresponding to the existence of a ...
    • Intersection problems in combinatorics 

      Brunk, Fiona (University of St Andrews, 2009-11-30) - Thesis
      With the publication of the famous Erdős-Ko-Rado Theorem in 1961, intersection problems became a popular area of combinatorics. A family of combinatorial objects is t-intersecting if any two of its elements mutually ...
    • Near-complete external difference families 

      Davis, James A.; Huczynska, Sophie; Mullen, Gary L. (2017-09) - Journal article
      We introduce and explore near-complete external difference families, a partitioning of the nonidentity elements of a group so that each nonidentity element is expressible as a difference of elements from distinct subsets ...
    • Pattern classes of permutations via bijections between linearly ordered sets 

      Huczynska, Sophie; Ruskuc, Nikola (2008-01) - Journal article
      A pattern class is a set of permutations closed under pattern involvement or, equivalently, defined by certain subsequence avoidance conditions. Any pattern class X which is atomic, i.e. indecomposable as a union of proper ...
    • Primitive free cubics with specified norm and trace 

      Huczynska, Sophie; Cohen, SD (2003-08) - Journal article
      The existence of a primitive free (normal) cubic x(3) ax(2) + cx b over a finite field F with arbitrary specified values of a (not equal 0) and b (primitive) is guaranteed. This is the most delicate case of a general ...
    • Well quasi-order in combinatorics : embeddings and homomorphisms 

      Huczynska, Sophie; Ruskuc, Nik (Cambridge University Press, 2015-07) - Conference item
      The notion of well quasi-order (wqo) from the theory of ordered sets often arises naturally in contexts where one deals with infinite collections of structures which can somehow be compared, and it then represents a useful ...