Split $(n+t)$-Color Partitions and Gordon-McIntosh Eight Order Mock Theta Functions

In 2004, the first author gave the combinatorial interpretations of four mock theta functions of Srinivasa Ramanujan using n-color partitions which were introduced by himself and G.E. Andrews in 1987. In this paper we introduce a new class of partitions and call them “split (n+t)-color partitions”. These new partitions generalize Agarwal–Andrews (n + t)-color partitions. We use these new combinatorial objects and give combinatorial meaning to two basic functions of Gordon-McIntosh found in 2000. They used these functions to establish the modular transformation formulas for certain eight order mock theta functions. The work done here has great potential for further research.