  This paper gives another proof of Propp and Roby's theorem saying that the
average antichain size in any reverse operator orbit of the poset $[m]\times
[n]$ is $\frac{mn}{m+n}$. It is conceivable that our method should work for
other situations. As a demonstration, we show that the average size of
antichains in any reverse operator orbit of $[m]\times K_{n-1}$ equals
$\frac{2mn}{m+2n-1}$. Here $K_{n-1}$ is the minuscule poset $[n-1]\oplus ([1]
\sqcup [1]) \oplus [n-1]$. Note that $[m]\times [n]$ and $[m]\times K_{n-1}$
can be interpreted as sub-families of certain root posets. We guess these root
posets should provide a unified setting to exhibit the homomesy phenomenon
defined by Propp and Roby.
