59 citations · 338 across the 95 of their papers we have counts for
8 papers · 1 filter
Using graphs to find the best block designs
R. A. Bailey, Peter J. Cameron
A statistician designing an experiment wants to get as much information as possible from the data gathered. Often this means the most precise estimate possible (that is, an estimat…
Three-factor decompositions of with the three generators in arithmetic progression
P. J. Cameron, D. A. Preece
Irrespective of whether n is prime, prime power with exponent >1, or composite, the group U_n of units of Z_n can sometimes be obtained as the direct product of cyclic groups gener…
Remoteness of permutation codes
Peter J. Cameron, Maximilien Gadouleau
In this paper, we introduce a new parameter of a code, referred to as the remoteness, which can be viewed as a dual to the covering radius. Indeed, the remoteness is the minimum ra…
Combinatorial representations
Peter J. Cameron, Maximilien Gadouleau, Søren Riis
This paper introduces combinatorial representations, which generalise the notion of linear representations of matroids. We show that any family of subsets of the same cardinality h…
Dixon's Theorem and random synchronization
Peter J. Cameron
A transformation monoid on a set Omega is called synchronizing if it contains an element of rank 1 (that is, mapping the whole of Omega to a single point). In this paper, I tackle…
An analogue of Ryser's Theorem for partial Sudoku squares
P. J. Cameron, A. J. W. Hilton, E. R. Vaughan
In 1956 Ryser gave a necessary and sufficient condition for a partial latin rectangle to be completable to a latin square. In 1990 Hilton and Johnson showed that Ryser's condition…