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.