4 citations · 11 across the 23 of their papers we have counts for
29 papers
Six Permutation Patterns Force Quasirandomness
Gabriel Crudele, Peter Dukes, Jonathan A. Noel
A sequence of permutations is said to be "quasirandom" if the induced density of every permutation in converges to as . We prove that…
Extremal Bounds for Three-Neighbour Bootstrap Percolation in Dimensions Two and Three
Peter J. Dukes, Jonathan A. Noel, Abel E. Romer
For , the -neighbour bootstrap process in a graph starts with a set of infected vertices and, in each time step, every vertex with at least infected neighbours b…
Families of modular arithmetic progressions with an interval of distance multiplicities
Peter J Dukes, Tao Gaede
Given a family of subsets of , define to be the multiset of all (cyclic) distances dist, where $\{x,y\} \subset…
Constructions of Sarvate-Beam Group Divisible Designs
Peter J. Dukes, Joanna Niezen
A balanced incomplete block design is a set system in which all pairs of distinct elements occur with a constant frequency. By contrast, a Sarvate-Beam design induces an interval o…
Balancing permuted copies of multigraphs and integer matrices
Coen del Valle, Peter J. Dukes
Given a square matrix over the integers, we consider the -module generated by the set of all matrices that are permutation-similar to . Motivated by analog…
An Update on the Existence of Kirkman Triple Systems with Subdesigns
Peter Dukes, Esther Lamken
A Kirkman triple system of order , KTS, is a resolvable Steiner triple system on elements. In this paper, we investigate an open problem posed by Doug Stinson, namely t…
Number cubes with consecutive line sums
Peter Dukes, Joanna Niezen
We settle the existence of certain "anti-magic" cubes using combinatorial block designs and graph decompositions to align a handful of small examples.
Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields
Peter J. Dukes, Xavier Martínez-Rivera
The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric matrix is defined as , where $\ell_j…
Local Balance in Graph Decompositions
Flora C. Bowditch, Peter J. Dukes
In a balanced graph decomposition, every vertex of the host graph appears in the same number of blocks. We propose the use of colored loops as a framework for unifying various othe…
On the Algebraic Combinatorics of Injections and its Applications to Injection Codes
Peter J. Dukes, Ferdinand Ihringer, Nathan Lindzey
We consider the algebraic combinatorics of the set of injections from a -element set to an -element set. In particular, we give a new combinatorial formula for the spherical…
On the minimum degree required for a triangle decomposition
Peter J. Dukes, Daniel Horsley
We prove that, for sufficiently large , every graph of order with minimum degree at least has a fractional edge-decomposition into triangles. We do this by refining…
Some new block designs of dimension three
Coen del Valle, Peter J. Dukes
The dimension of a block design is the maximum positive integer such that any of its points are contained in a proper subdesign. Pairwise balanced designs PBD have d…
Leaves for packings with block size four
Yanxun Chang, Peter J. Dukes, Tao Feng
We consider maximum packings of edge-disjoint -cliques in the complete graph . When or , these are simply block designs. In other congruence class…
A lower bound on permutation codes of distance
Sergey Bereg, Peter Dukes
A classical recursive construction for mutually orthogonal latin squares (MOLS) is shown to hold more generally for a class of permutation codes of length and minimum distance…
Constructions and uses of incomplete pairwise balanced designs
Peter J. Dukes, Esther R. Lamken
We give explicit constructions for incomplete pairwise balanced designs IPBD, or, equivalently, edge-decompositions of a difference of two cliques in…
Incidence structures near configurations of type
Peter Dukes, Kaoruko Iwasaki
An configuration is an incidence structure equivalent to a linear hypergraph on vertices which is both 3-regular and 3-uniform. We investigate a variant in which one co…
On the cone of weighted graphs generated by triangles
Coen del Valle, Peter Dukes, Kseniya Garaschuk
Motivated by problems involving triangle-decompositions of graphs, we examine the facet structure of the cone of weighted graphs on vertices generated by triangles. Our r…
Fractional triangle decompositions of dense 3-partite graphs
Flora C. Bowditch, Peter J. Dukes
We compute a minimum degree threshold sufficient for 3-partite graphs to admit a fractional triangle decomposition. Together with recent work of Barber, Kühn, Lo, Osthus and Taylor…
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…
Semidefinite programming for permutation codes
Mathieu Bogaerts, Peter Dukes
We initiate study of the Terwilliger algebra and related semidefinite programming techniques for the conjugacy scheme of the symmetric group Sym. In particular, we compute orb…