An interesting q-series related to the 4th symmetrized rank function

This paper presents the method to utilizing the s-fold extension of Bailey's lemma to obtain spt-type functions related to the symmetrized rank function η2k(n). We provide the k=2 example, but clearly illustrate how deep connections between higher-order spt functions exist for any integer k>1, and provide several directions for possible research. In particular, we present why the function sptM∗(n), the total number of appearances of the smallest parts of partitions where parts greater than the smallest plus M do not occur, is an spt function that appears to have central importance. We also make note about extending spt-type functions to partition pairs.