An elementary non-recursive expression for the partition function P(n)

TL;DR

This paper presents a new non-recursive formula for calculating the number of irreducible representations of the symmetric group, based on partition classification, offering a potentially simpler computational approach.

Contribution

It introduces an elementary, non-recursive expression for the partition function related to symmetric group representations, expanding on previous recursive methods.

Findings

Derived a non-recursive formula for P(n)

Connected partition classification to irreducible representations

Published in Physica 1982, with improved introduction

Abstract

Consideration of a classification of the number of partitions of a natural number according to the members of sub-partitions differing from unity leads to a non-recursive formula for the number of irreducible representations of the symmetric group Sn. This article was published, long ago, under the title A non-recursive expression for the number of irreducible representations of the Symmetric Group Sn, Physica 114A, 1982, 361-364, North-Holland Publishing Co. The Introduction has been, somewhat, improved, however, the handmade result remains unproved.