### Ample & pristine numbers

Parallels between the perfect and abundant numbers and their recursive analogs point to deeper structure in the recursive divisor function.

### Recursively divisible numbers

Recursively divisible numbers are a new kind of number that are highly divisible, whose quotients are highly divisible, and so on.

### The mathematical structure of innovation

A theoretical model of recursive innovation suggests that new technologies are recursively built up from new combinations of existing ones.

### Resolution of ranking hierarchies in directed networks

Identifying ranking hierarchies in complex networks is of paramount importance in many disciplines and applications

### Serendipity and strategy

In systems of innovation, the relative usefulness of different components changes as the number of components we possess increases.

### Transference for the Erdős-Ko-Rado theorem

Two constructions for an intersecting family of r-sets.

### Assessing self-assembly

The information needed to self-assemble a structure quantifies its modularity and explains the prevalence of certain structures over others.

### Strategy for conkers

In single elimination competition the best indicator of success is a player's wealth: the accumulated wealth of all defeated players.