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Recently, Blecher and Knopfmacher explored the notion of fixed points ininteger partitions and hypothesized on the relative number of partitions withand without a fixed point. We resolve their open question by working fixedpoints into a growing number of interconnected partition statistics involvingFrobenius symbols, Dyson's crank, and the mex (minimal excluded part). Also, wegeneralize the definition of fixed points and connect that expanded notion tothe $\text{mex}_j$ defined by Hopkins, Sellers, and Stanton as well as the$j$-Durfee rectangle defined by Hopkins, Sellers, and Yee.

On Blecher and Knopfmacher's Fixed Points for Integer Partitions