  Wilf partitions are partitions of an integer $n$ in which all nonzero
multiplicities are distinct. On his webpage, the late Herbert Wilf posed the
problem to find "any interesting theorems" about the number f(n) of those
partitions. Recently, Fill, Janson and Ward (and independently Kane and
Rhoades) determined an asymptotic formula for $\log f(n)$. Since the original
motivation for studying Wilf partitions was the fact that the operation that
interchanges part sizes and multiplicities is an involution on the set of Wilf
partitions, they mentioned as an open problem to determine a similar asymptotic
formula for the number of fixed points of this involution, which we denote by
F(n). In this short note, we show that the method of Fill, Janson and Ward also
applies to F(n). Specifically, we obtain the asymptotic formula $\log F(n) \sim
\frac12 \log f(n)$.
