  In a paper by the author, Hemmer, Hopkins, and Keith the concept of a fixed
point in a sequence was applied to the sequence of first column hook lengths of
a partition. In this paper we generalize this notion to fixed hook lengths in
an arbitrary column of a partition. We establish combinatorial connections
between these fixed hooks and colored partitions that have interesting gap and
mex-like conditions. Additionally, we obtain several generating functions for
hook lengths of a given fixedness by hook length or part size in unrestricted
partitions as well as some classical restrictions such as odd and distinct
partitions.
