A universal cycle for a set $S$ is a cyclic string of length $|S|$ in which all members of $S$ are represented once and only once by a substring of a given length $k$. In this presentation, a new method is shown for creating universal cycles for the permutations of an $n$-set in their shorthand form. Twelve variations of this method are provided, producing twelve different universal cycles.

This work was performed under the supervision of professor Joe Sawada, and supported by an Aboriginal Undergraduate Research Award.