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 related ...

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 number ...

In 1944, Freeman Dyson defined the concept of rank of an integer partition and introduced without definition the term of crank of an integer partition. A definition for the crank satisfying the ...