  In this paper, we consider the asymptotic properties of hook numbers of
partitions in restricted classes. More specifically, we compare the frequency
with which partitions into odd parts and partitions into distinct parts have
hook numbers equal to $h \geq 1$ by deriving an asymptotic formula for the
total number of hooks equal to $h$ that appear among partitions into odd and
distinct parts, respectively. We use these asymptotic formulas to prove a
recent conjecture of the first author and collaborators that for $h \geq 2$ and
$n \gg 0$, partitions into odd parts have, on average, more hooks equal to $h$
than do partitions into distinct parts. We also use our asymptotics to prove
certain probabilistic statements about how hooks distribute in the rows of
partitions.

Combinatorics;Number Theory