perm filename ABST.829[BIB,CSR] blob sn#568236 filedate 1981-03-03 generic text, type C, neo UTF8

COMMENT ⊗ VALID 00002 PAGES C REC PAGE DESCRIPTION C00001 00001 C00002 00002 STAN-CS-80-829 C00004 ENDMK C⊗; 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.