  Recall that an excedance of a permutation $\pi$ is any position $i$ such that
$\pi_i > i$. Inspired by the work of Hopkins, McConville and Propp (Elec. J.
Comb., 2017) on sorting using toppling, we say that a permutation is toppleable
if it gets sorted by a certain sequence of toppling moves. One of our main
results is that the number of toppleable permutations on $n$ letters is the
same as those for which excedances happen exactly at $\{1,\dots, \lfloor
(n-1)/2 \rfloor\}$. Additionally, we show that the above is also the number of
acyclic orientations with unique sink (AUSOs) of the complete bipartite graph
$K_{\lceil n/2 \rceil, \lfloor n/2 \rfloor + 1}$. We also give a formula for
the number of AUSOs of complete multipartite graphs. We conclude with
observations on an extremal question of Cameron et al. concerning maximizers of
(the number of) acyclic orientations, given a prescribed number of vertices and
edges for the graph.
