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

2014/07/21 by Cristina Ballantine, Ballantine, Cristina, Mircea Merca +1
Mathematics · #05A17 #05A19 #05A20 #11B39 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:05A17 #msc:05A19 #msc:05A20 #msc:11B39

paper · pdf · doi:10.48550/arxiv.1407.5552

15 pages, improved argument that sequence of upper bounds in Theorem 5 is decreasing

arxiv created 2014/08/06 · arxiv updated 2014/08/07

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.

Related

• Fibonacci-like property of partition function
• Power Partitions and Semi-m-Fibonacci Partitions
• On Fibonacci partitions
• Arndt and De Morgan Integer Compositions
• On Zeckendorf Related Partitions Using the Lucas Sequence