  We present an initial-seed-mutation formula for d-vectors of cluster
variables in a cluster algebra. We also give two rephrasings of this recursion:
one as a duality formula for d-vectors in the style of the g-vectors/c-vectors
dualities of Nakanishi and Zelevinsky, and one as a formula expressing the
highest powers in the Laurent expansion of a cluster variable in terms of the
d-vectors of any cluster containing it. We prove that the initial-seed-mutation
recursion holds in a varied collection of cluster algebras, but not in general.
We conjecture further that the formula holds for source-sink moves on the
initial seed in an arbitrary cluster algebra, and we prove this conjecture in
the case of surfaces.
