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

  • A.K. Agarwal
  • G. Sood
Keywords: Mock theta functions, (n t)-color partitions, split (n t)- color partitions, combinatorial interpretations.


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 a great potential for future research.

Author Biography

A.K. Agarwal, Panjab University, Chandigarh

Emeritus Scientist, CSIR

Centre for Advanced Study in Mathematics

Panjab University, Chandigarh-160014

Article Number