  The main result of this paper is to show that all binomial identities are
orderable. This is a natural statement in the combinatorial theory of finite
sets, which can also be applied in distributed computing to derive new strong
bounds on the round complexity of the weak symmetry breaking task.
  Furthermore, we introduce the notion of a fundamental binomial identity and
find an infinite family of values, other than the prime powers, for which no
fundamental binomial identity can exist.
