  In 2009, Chmutov introduced the partial-duality for a ribbon graph $G$.
Recently, Gross, Mansour and Tucker enumerated all possible partial-duals of
$G$ by genus and introduced the partial-dual genus polynomial of a ribbon graph
$G.$ This paper mainly enumerates partial-duals for planar ribbon graphs.
First, we obtain a formula for the maximum partial-dual genus for any planar
ribbon graph and give a negative answer to the interpolating conjecture of
Gross, Mansour and Tucker. Then we show that there is a recurrence relation
between the partial-dual genus polynomials of planar ribbon graphs $G-e$ and
$G$. Furthermore, two related results are also given. These recurrence
relations give new approaches to calculate the partial-genus dual polynomials
for some planar ribbon graphs. In addition, we prove the asymptotic normality
for some partial-dual genus distributions.
