  We discuss results dealing with universal cycles (u-cycles) and $s$-overlap
cycles, and contribute to the body of those results by proving existence of
universal cycles of naturally labeled posets (NL posets), $s$-overlap cycles of
words of weight $k$, and juggling patterns. The result on posets is, to the
best of our knowledge, the first demonstration of the existence of a u-cycle
whose length is unknown.
