n people are seated randomly at a rectangular table with ⌊n/2⌋ and ⌈n/2⌉ seats along the two opposite sides for two
dinners. What's the probability that neighbors at the first dinner are no more
neighbors at the second one? We give an explicit formula and we show that its
asymptotic behavior as n goes to infinity is e−2(1+4/n) (it is known
that it is e−2(1−4/n) for a round table). A more general permutation
problem is also considered.Comment: 10 page