  Interval parking functions (IPFs) are a generalization of ordinary parking
functions in which each car is willing to park only in a fixed interval of
spaces. Each interval parking function can be expressed as a pair $(a,b)$,
where $a$ is a parking function and $b$ is a dual parking function. We say that
a pair of permutations $(x,y)$ is \emph{reachable} if there is an IPF $(a,b)$
such that $x,y$ are the outcomes of $a,b$, respectively, as parking functions.
Reachability is reflexive and antisymmetric, but not in general transitive. We
prove that its transitive closure, the \emph{pseudoreachability order}, is
precisely the bubble-sort order on the symmetric group $\Sym_n$, which can be
expressed in terms of the normal form of a permutation in the sense of
du~Cloux; in particular, it is isomorphic to the product of chains of lengths
$2,\dots,n$. It is thus seen to be a special case of Armstrong's sorting order,
which lies between the Bruhat and (left) weak orders.
