Each simply generated family of trees is unambiguously
associated with another simply generated family
of trees
such that the total weight of the trees with
leaves in
is equal to the total weight of the leftist trees with
leaves in
. This interrelation induces a partition
on
the set of trees with
leaves appearing in
such that
each block
is associated with exactly one leftist
tree
with
leaves. Given
(resp.
), we shall establish an explicit transformation
defined on the trees for the construction of
(resp.
). The
presented approach implies a compressed representation of a simply
generated family of trees with
leaves by leftist simply generated
trees with the same number of leaves.