Circular seating arrangements

Abstract

This problem concerns n couples around a circular table, husbands and wives seated alternately. The number of ways in which the n couples can be seated such that no husband and wife sit next to each other is required. This problem is not covered in the standard texts such as Feller (1950) or Whitworth (1901) who concentrate on the simpler linear problem, i.e. seating arrangements in a row. In this paper we obtain a solution for the circular problem, deriving thereby the probability that no such matching occurs when the seating is made at random, and showing finally that this probability has a limiting value when n is large.