  We define the disposition polynomial $R_{m}(x_1, x_2, ..., x_n)$ as
$\prod_{k=0}^{m-1}(x_1+x_2+...+x_n+k)$. When $m=n-1$, this polynomial becomes
the generating function of plane trees with respect to certain statistics as
given by Guo and Zeng. When $x_i=1$ for $1\leq i\leq n$, $R_{m}(x_1, x_2, ...,
x_n)$ reduces to the rising factorial $n(n+1)... (n+m-1)$. Guo and Zeng asked
the question of finding a combinatorial proof of the formula for the generating
function of plane trees with respect to the number of younger children and the
number of elder children. We find a combinatorial interpretation of the
disposition polynomials in terms of the number of right-to-left minima of each
linear order in a disposition. Then we establish a bijection between plane
trees on $n$ vertices and dispositions from ${1, 2,..., n-1}$ to ${1, 2,...,
n}$ in the spirit of the Pr\"ufer correspondence. It gives an answer to the
question of Guo and Zeng, and it also provides an answer to another question of
Guo and Zeng concerning an identity on the plane tree expansion of a polynomial
introduced by Gessel and Seo.
