We analyze Jim Proppâ€™s P -machine, a simple deterministic process that simulates a random walk on Zd to within a constant. The proof of the error bound relies on several estimates in the theory ofâ€¦ (More)

For a fixed graph H, a graph G is uniquely H-saturated if G does not contain H, but the addition of any edge from G to G completes exactly one copy of H. Using a combination of algebraic methods andâ€¦ (More)

Consider the following problem: how many collinear triples of points must a transversal of ZnÃ—Zn have? This question is connected with venerable issues in discrete geometry. We show that the answer,â€¦ (More)

We show that Î» is an eigenvalue of a k-uniform hypertree (k > 3) if and only if it is a root of a particular matching polynomial for a connected induced subtree. We then use this to provide aâ€¦ (More)

A de Bruijn covering code is a q-ary string S so that every qary string is at most R symbol changes from some n-word appearing consecutively in S. We introduce these codes and prove that they canâ€¦ (More)

Persuasive energy monitoring technology has the potential to inspire sustainable energy lifestyles within the home. However, to effect positive ecological behaviour change, a more user-drivenâ€¦ (More)