Chromatic Solutions, II

Source abstract

This paper is a continuation of the Waterloo Research Report CORR 81-12, (see [ 1 ]) referred to in what follows as I. That Report is entitled “Chromatic Solutions”. It is largely concerned with a power series h in a variable z 2 , in which the coefficients are polynomials in a “colour number” λ . By definition the coefficient of z 2 r , where r > 0, is the sum of the chromatic polynomials of the rooted planar triangulations of 2 r faces. (Multiple joins are allowed in these triangulations.) Thus for a positive integral λ the coefficient is the number of λ -coloured rooted planar triangulations of 2 r faces. The use of the symbol z 2 instead of a simple letter t is for the sake of continuity with earlier papers. In I we consider the case (1) where n is an integer exceeding 4.