Generalization of formulas for partition functions

Abstract

The idea of formulas for partition functions dates back to Cayley and Macmahon to obtain traceable power series expressions, after which several extensions were made. In this paper, further extension was provided together with a generalized method of finding formulars for some partition functions. We also relate the technical results with their graphical interpretations through a novel use of Bar Charts and Scatter diagrams. We generalized a method of finding formulas for some partition functions.