On partition polynomials and partition functions

2020/08/08 by Goubi, Mouloud
#05A17 #11P81 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2008.11122

Abstract

In this paper we revisit the work of E.T. Bell concerning partition polynomials in order to introduce the reciprocal partition polynomials. We give their explicit formulas and apply the result to compute closed formulae for some well-known partition functions.

Related

• Formulas for the number of k-colored partitions and the number of plane partitions of n in terms of the Bell polynomials
• Simple proofs and expressions for the restricted partition function and its polynomial part
• Closed-Form Formula for the Partition Function and Related Functions
• An Alternative Generating Function for k-Regular Partitions
• Combinatorial Formula for the Partition Function