Inequalities involving the generating function for the number of partitions into odd parts

TL;DR

This paper explores inequalities relating the generating function for partitions into odd parts with that for odd divisors, using Fibonacci numbers expressed via multinomial coefficients.

Contribution

It introduces a new family of double inequalities connecting partition generating functions and divisor functions, leveraging Fibonacci number representations.

Findings

Established inequalities between generating functions for partitions and divisors

Connected Fibonacci numbers with multinomial coefficients and partition functions

Provided a novel analytical framework for partition-related inequalities

Abstract

Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. We use this fact to introduce a family of double inequalities involving the generating function for the number of partitions into odd parts and the generating function for the number of odd divisors.