Using GENERATINGFUNCTIONOLOGY to Enumerate Distinct-Multiplicity Partitions

TL;DR

This paper applies generating function techniques to enumerate distinct-multiplicity partitions, addressing a problem posed by Herbert Wilf and contributing to the combinatorial understanding of integer partitions.

Contribution

It introduces a novel generating function approach to count partitions with distinct multiplicities, advancing the combinatorial enumeration methods.

Findings

Derived explicit formulas for counting such partitions

Connected the enumeration to classical generating function techniques

Provided insights into Wilf's partition problem

Abstract

This article, written in fond memory of Herbert Saul Wilf (June 13, 1931- Jan. 7, 2012), explores integer partitions where each part shows up a different number of times than the other parts (if it shows up at least once), thereby making a modest contribution towards the solution of one of the eight intrigiung problems posted by Herb Wilf on his website on Dec. 13, 2010