Universal Cycles of Restricted Classes of Words

Arielle Leitner, Anant Godbole

Published 2008-08-08, updated 2009-04-20Version 2

It is well known that Universal Cycles of $k$-letter words on an $n$-letter alphabet exist for all $k$ and $n$. In this paper, we prove that Universal Cycles exist for restricted classes of words, including: non-bijections, equitable words (under suitable restrictions), ranked permutations, and "passwords".