Article

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

Published in: Quaestiones Mathematicae
Volume 40 , issue 3 , 2017 , pages: 319–332

DOI: 10.2989/16073606.2017.1287135

Author(s): Cristina Ballantine Department of Mathematics and Computer Science, USA , Mircea Merca Department of Mathematics, Romania

Keywords: 05A20 , 05A19 , 05A17 , 11B39 , 05A20 , 05A19 , 05A17 , 11B39

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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.

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