  Canon permutations are permutations of the multiset having $k$ copies of each
integer between $1$ and $n$, with the property that the subsequences obtained
by taking the $j$th copy of each entry, for each fixed $j$, are all the same.
For $k=2$, canon permutations are sometimes called nonnesting permutations, and
it is known that the polynomial that enumerates them by the number of descents
factors as a product of an Eulerian polynomial and a Narayana polynomial. We
extend this result to arbitrary $k$, and we relate the problem to the
enumeration of standard Young tableaux of rectangular shape with respect to
generalized descent statistics. Our proof is bijective, and it also settles a
conjecture of Sulanke about the distribution of certain lattice path
statistics.
