4 citations · 11 across the 23 of their papers we have counts for
4 papers · 1 filter
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…