  In this paper, we discuss a few recent conjectures made by George Beck
related to the ranks and cranks of partitions. The conjectures for the rank of
a partition were proved by Andrews by using results due to Atkin and
Swinnerton-Dyer on a suitable generating function, while the conjectures
related to cranks were studied by Shane Chern using weighted partition moments.
We revisit the conjectures on the crank of a partition by decomposing the
relevant generating function and further explore connections with Apple-Lerch
series and tenth order mock theta functions.
