The study of partition functions is a significant area in number theory, focusing on how integers can be expressed as sums of other integers. Recent research has explored various inequalities ...

Partition functions, which enumerate the distinct ways a positive integer may be expressed as a sum of positive integers, have long captivated mathematicians due to their deep connections with ...

In this paper, we introduce truncated forms for two theta identities involving the generating functions for partitions with non-negative rank and non-negative crank. As corollaries we derive new ...