USAJMO 2026 Question 2

There are $m$ foxes and $n$ bunnies in $m+n$ seats around a circular table, all distinguishable. A neighboring fox and bunny may swap positions. From a fixed starting configuration, determine the number of configurations reachable by a sequence of swaps. Rotations and reflections are considered distinct.

Proposed by Milan Haiman.

Manual essay; 1 editorial point, not official contest scoring.