  Motivated by a recent paper of Straub, we study the distribution of integer
partitions according to the length of their largest hook, instead of the usual
statistic, namely the size of the partitions. We refine Straub's analogue of
Euler's Odd-Distinct partition theorem, derive a generalization in the spirit
of Alder's conjecture, as well as a curious analogue of the first
Rogers-Ramanujan identity. Moreover, we obtain a partition theorem that is the
counterpart of Euler's pentagonal number theory in this setting, and connect it
with the Rogers-Fine identity. We concludes with some congruence properties.
