A review of enumeration methods on integer partition

Abstract

A partition of a non-negative integer is a way of writing as a sum of a non-decreasing sequence of parts. The paper provides the study of some properties of integer partitions. In particular, we are interested to show the number of partitions of in which the summand appears at most times is equal to the number of partitions in which the part appears any times and the other part appears at most times by using a generating function and algebraic construction.