Geometrical constraints on Bennett's predictions of chromosome order

Two aspects of the Bennett model are of interest from a mathematical point of view. First there is the question whether Bennett's "ranking method" for predicting the order of chromosomes will always work. The answer depends on the number n of chromosomes: if n is odd, predictions (being not necessarily unique) are possible in most cases. Secondly there is Bennett's procedure for determining the arrangement of chromosomes. It is shown that the method of minimising the perimeter of the polygon obtained by connecting the centromeres is only applicable if the positions of the n centromeres do not deviate too much from an arrangement along a regular n-gon.