Technical Terms Chromatic Symmetric Function: A symmetric function that sums over proper colourings of a graph, generalising the chromatic polynomial and encapsulating graph invariants.

HUILAN LI, TRUEMAN MACHENRY, THE CONVOLUTION RING OF ARITHMETIC FUNCTIONS AND SYMMETRIC POLYNOMIALS, The Rocky Mountain Journal of Mathematics, Vol. 43, No. 4 (2013), pp. 1227-1259 ...