Today at tea, some grad students were discussing the following enumeration problem:
How many elements of have zeroes in all diagonal entries?
I think they [Redacted]. The answer is apparently known but classified. It’s a sort of q-analog of derangements (i.e., permutations without fixed points), but if you take the derangement formula and add q-numbers in the naive way, the formula doesn’t seem to work for n > 2.