# Journal of the Ramanujan Mathematical Society

Volume 35, Issue 3, September 2020 pp. 263–276.

On the treatment of partitions as factorization and further analysis

**Authors**:
Abhimanyu Kumar and Meenakshi Rana

**Author institution:**Electrical and Instrumentation Engineering Department, Thapar Institute of Engineering and Technology, Patiala 147004, Punjab, India

**Summary: **
The norm of an integer partition is defined as the product of the
parts of that partition. This paper aims to study the norms of the
integer partitions and their relation to primes. Observing that
the same norm value sometimes appears for different partitions,
the norm counting function r(i,n) is defined and investigated.
Its generating function is proved which unravels various
properties, bounds and recursive relations as well as deep
connections with both multiplicative and additive partitions.
Later, a formula for the norm counting function is given and the
error bounds are provided. This analysis instigates the
development of an asymptotic formula for the number of
multiplicative partitions of n based on heuristic assumptions.

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