  We consider an operator of Bernstein for symmetric functions, and give an
explicit formula for its action on an arbitrary Schur function. This formula is
given in a remarkably simple form when written in terms of some notation based
on the code of a partition. As an application, we give a new and very simple
proof of a classical result for the KP hierarchy, which involves the Plucker
relations for Schur function coefficients in a tau function for the hierarchy.
This proof is especially compact because of a restatement that we give for the
Plucker relations that is symmetrical in terms of partition code notation.
