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

2014; Electronic Journal of Combinatorics; Volume: 21; Issue: 2 Linguagem: Inglês

10.37236/3726

1097-1440

A. K. Agarwal, G. Sood,

Analytic Number Theory Research

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.