Chromatic sums revisited
This paper is a unified reworking of a series of eight papers by the author from 1973 to 1982 on chromatic sums. The question of original interest to the author was: How many \(\lambda\)-colored rooted planar triangulations are there with \(2n\) triangles. The study of generating functions and associated functional equations for these numbers and related problems led the author into an extensive analytical journey, with particular attention to the following two functional equations \[ xg= x^3 y \lambda(\lambda- 1)+ \lambda^{- 1} yz gq+ yz(g- x^2 L)- x^2 y^2 z \Delta g, \] \[ H''\{2t+ 5H- 3t H'\}= 48t\qquad (t= z^2). \]
scientific article; zbMATH DE number 794225