BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-80-829
       ENTRY:: June 08, 1995
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: The dinner table problem
        TYPE:: Technical Report
      AUTHOR:: Aspvall, Bengt
      AUTHOR:: Liang, Frank M.
        DATE:: December 1980
       PAGES:: 14
    ABSTRACT:: This report contains two papers inspired by the "dinner table
               problem": If n 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 $e^{-2}$ as $n \rightarrow \infty$,
               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.
       NOTES:: [Adminitrivia V1/Prg/19950608]
         END:: STAN//CS-TR-80-829