  In this paper, we generalize a few important results in Integer Partitions;
namely the results known as Stanley's theorem and Elder's theorem, and the
congruence results proposed by Ramanujan for the partition function. We
generalize the results of Stanley and Elder from a fixed integer to an array of
subsequent integers, and propose an analogue of Ramanujan's congruence
relations for the `number of parts' function instead of the partition function.
We also deduce the generating function for the `number of parts', and relate
the technical results with their graphical interpretations through a novel use
of the Ferrer's diagrams.
