In this paper, we have derived a generating function for a restricted partition function. This is in conjunction with two identities of Euler provides a new partition theoretic interpretation of two identities of Euler.
The generating function for a restricted partition function is derived. This in conjunction with two identities of Rogers provides new partition theoretic interpretations of Rogers-Ramanujan identities.
Given a set of positive integers $ A = \{ a_{1} , \dots , a_{n} \} $, we study the number $ p_{A} (t) $ of nonnegative integer solutions $ \left( m_{1} , \dots , m_{n} \right) $ to $ \sum_{j=1}^{n} m_{j} a_{j} = t $. We derive an explicit formula for the polynomial part of $p_A$.
Untrodden pathways in the theory of the restricted partition function p(n,N)
