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STAN-CS-80-829
The Dinner Table Problem
by Bengt Aspvall and Frank Liang (13 pages, December 1980)

	This report contains two papers inspired by the "dinner table problem":
If %2n%1 people are seated randomly around a circular table for two meals, what is
the probability that no two people sit together at both meals?  We show that
this probability approaches  %2e∩[-2]%1 as  %2n → %5α∞%1, and also give a closed form.  We
then observe that in many similar problems on permutations with restricted
position, the number of permutations satisfying a given number of properties is
approximately Poisson distributed.  We generalize our asymptotic argument to
prove such a limit theorem, and mention applications to the problems of
derangements, menages, and the asymptotic number of Latin rectangles.