Partitions with Distinct Multiplicities of Parts: On An "Unsolved Problem" Posed By Herbert Wilf

James Allen Fill, Svante Janson, Mark Daniel Ward

Abstract


Wilf's Sixth Unsolved Problem asks for any interesting properties of the set of partitions of integers for which the (nonzero) multiplicities of the parts are all different.  We refer to these as Wilf partitions.  Using $f(n)$ to denote the number of Wilf partitions, we establish lead-order asymptotics for $\ln{f(n)}$.

 


Keywords


asymptotic enumeration, partitions of integers, Wilf partitions

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