Identifying an appropriate set of " observables " is a nontrivial task for most approaches to quantum gravity. We describe how it may be accomplished in the context of a recently proposed family of… (More)

The “generic” family of classical sequential growth dynamics for causal sets [?] provides cosmological models of causal sets which are a testing ground for ideas about the, as yet unknown, quantum… (More)

Let X be an n–element finite set, 0 < k < n/2 an integer. Suppose that {A1, B1} and {A2, B2} are pairs of disjoint k-element subsets of X (that is, |A1| = |B1| = |A2| = |B2| = k,A1 ∩ B1 = ∅, A2 ∩ B2… (More)

Körner and Malvenuto asked whether one can find ( n n/2 ) linear orderings (i.e., permutations) of the first n natural numbers such that any pair of them places two consecutive integers somewhere in… (More)

We study the basic preferential attachment process, which generates a sequence of random trees, each obtained from the previous one by introducing a new vertex and joining it to one existing vertex,… (More)

Non-perturbative theories of quantum gravity inevitably include configurations that fail to resemble physically reasonable spacetimes at large scales. Often, these configurations are entropically… (More)

The “generic” family of classical sequential growth dynamics for causal sets [1] provides cosmological models of causal sets which are a testing ground for ideas about the, as yet unknown, quantum… (More)

Is there, for all large values of n, a graph on n vertices with no clique of size 5 log n, and no independent set of size 5 log n? Is there a graph with some number n of vertices, no cycles of length… (More)

We prove that there is a constant c > 0, such that whenever p ≥ n, with probability tending to 1 when n goes to infinity, every maximum triangle-free subgraph of the random graph Gn,p is bipartite.… (More)

We have not made any arrangements for lunch; there are several convenient possibilities on and near campus. • There is a self-service cafeteria on the second floor of the Staff House (R24 on the… (More)