In the past two decades, there have been far-reaching developments in the problem of determining all finite non-abelian simple groupsâ€”so much so, that many people now believe that the solution to theâ€¦ (More)

We study the covering radius of sets of permutations with respect to the Hamming distance. Let f(n, s) be the smallest number m for which there is a set of m permutations in Sn with covering radius râ€¦ (More)

We study relational structures (especially graphs and posets) which satisfy the analogue of homogeneity but for homomorphisms rather than isomorphisms. The picture is rather different. Our mainâ€¦ (More)

Let Sn be the symmetric group on the set X = {1,2, .....,n}. A subsetS of Sn is intersectingif for any two permutationsg andh in S, g(x) = h(x) for somexâˆˆ X (that isg andh agreeon x). M. Deza and P.â€¦ (More)

This chapter surveys automorphisms of finite graphs, concentrating on the asymmetry of typical graphs, prescribing automorphism groups (as either permutation groups or abstract groups), and specialâ€¦ (More)

Peter J. Cameron, Michael W. Newman, âˆ— Ashley Montanaro, Simone Severini, â€ and Andreas Winter School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, U.K. Department ofâ€¦ (More)

Our main topic is the number of subsets of 1; n] which are maximal with respect to some condition such as being sum-free, having no number dividing another, etc. We also investigate some relatedâ€¦ (More)