Counting racks of order n

Matthew Ashford, Oliver Riordan

A rack on $[n]$ can be thought of as a set of maps $(f_x{)}_{x\in [n]}$, where each $f_x$ is a permutation of $[n]$ such that $f_{(x)f_y}=f_y^{-1}{f}_x{f}_y$ for all $x$ and $y$. In 2…