@article{ajams2014265,
author={Das, Sabuj},
title={Some Restricted Partition Functions},
journal={American Journal of Applied Mathematics and Statistics},
volume={2},
number={6},
pages={386--393},
year={2014},
url={http://pubs.sciepub.com/ajams/2/6/5},
issn={2333-4576},
abstract={In 1742, Euler found the generating function for P(n). Hardy said Ramanujan was the first, and upto now the only, Mathematician to discover any such properties of P(n). In 1952, Macmahon established a table of P(n) for the first 200 values of n. This paper showed how to find the number of partition of n by using Macmahon¡¯s table. In 1742, Euler also stated the series in the enumeration of partitions. This Paper showed how to generate the Euler¡¯s use of series in the enumeration of partitions. In 1952, Macmahon also quoted the self-conjuate partitions of n. In this Paper, Macmahon¡¯s self-conjugate partitions are explained with the help of array of dots. This paper showed how to prove the Euler¡¯s Theorems with the help of Euler¡¯s device of the introduction of a second parameter z, and showed how to prove the Theorem 3 with the help of Euler¡¯s generating function for P(n), and also showed how to prove the Theorem 4 with the help of certain conditions of P(n).},
doi={10.12691/ajams-2-6-5}
publisher={Science and Education Publishing}
}