  We give an alternative construction for a family of partition generating
functions due to Kanade and Russell. In our alternative construction, we use
ordinary partitions instead of jagged partitions. We also present new
generating functions which are evidently positive series for partitions due to
Kanade and Russell. To obtain those generating functions, we first construct an
evidently positive series for a key infinite product. In that construction, a
series of combinatorial moves is used to decompose an arbitrary partition into
a base partition together with some auxiliary partitions that bijectively
record the moves.
