4 citations · 11 across the 23 of their papers we have counts for
5 papers · 1 filter
Pairwise balanced designs covered by bounded flats
Nicholas M. A. Benson, Peter J. Dukes
We prove that for any and , there exist, for all sufficiently large admissible , a pairwise balanced design PBD of dimension for which all -point-generated…
Mutually orthogonal latin squares with large holes
Peter J. Dukes, Christopher M. van Bommel
Two latin squares are orthogonal if, when they are superimposed, every ordered pair of symbols appears exactly once. This definition extends naturally to `incomplete' latin squares…
Threefold triple systems with nonsingular
Peter J. Dukes, Kseniya Garaschuk
There are various results connecting ranks of incidence matrices of graphs and hypergraphs with their combinatorial structure. Here, we consider the generalized incidence matrix $N…
Generalized laminar families and certain forbidden matrices
Peter Dukes
Recall that in a laminar family, any two sets are either disjoint or contained one in the other. Here, a parametrized weakening of this condition is introduced. Let us say that a s…
Pairwise balanced designs with prescribed minimum dimension
Peter J. Dukes, Alan C. H. Ling
The dimension of a linear space is the maximum positive integer such that any of its points generate a proper subspace. For a set of integers at least two, recall that…