In the past two decades, there have been far-reaching developments in the problem of determining all finite non-abelian simple groups—so much so, that many people now believe that the solution to the… Expand

We study relational structures (especially graphs and posets) which satisfy the analogue of homogeneity but for homomorphisms rather than isomorphisms.Expand

Preface 1. What is combinatorics? 2. On numbers and counting 3. Subsets, partitions, permutations 4. Recurrence relations and generating functions 5. The principle of inclusion and exclusion 6. Latin… Expand

We find that the same sequence of integers counts two families of things with no obvious connection, or that a simple translation connects the answers to two counting problems.Expand

We present a new treatment of the permutation f of antichains in ranked posets moving the set of lower units of a monotone Boolean function to theSet of its upper zeros.Expand