All binomial identities are orderable

In this paper we show that all binomial identities are orderable. This is a natural statement from the combinatorial theory of finite sets which additionally has applications in distributed computing. Specifically, we are able to obtain new strong bounds on the round complexity of the weak symmetry breaking task. 1. Preliminaries For any natural number n, we set [n] := {1, . . . , n}. Definition 1.1. A binomial identity is any equality (1.1) ( n a1 ) + · · · + ( n ak ) = ( n b1 ) + · · · + ( n bm )