  We study a family of identities regarding a divisibility property of the
Kostant partition function which first appeared in a paper of Baldoni and
Vergne. To prove the identities, Baldoni and Vergne used techniques of residues
and called the resulting divisibility property "mysterious." We prove these
identities entirely combinatorially and provide a natural explanation of why
the divisibility occurs. We also point out several ways to generalize the
identities.
