Universal Cycles of Discrete Functions
Combinatorics
2012-04-12 v1
Abstract
A connected digraph in which the in-degree of any vertex equals its out-degree is Eulerian; this baseline result is used as the basis of existence proofs for universal cycles (also known as deBruijn cycles or -cycles) of several combinatorial objects. We present new results on the existence of universal cycles of certain classes of functions. These include onto functions, and 1-inequitable sequences on a binary alphabet. In each case the connectedness of the underlying graph is the non-trivial aspect to be established.
Keywords
Cite
@article{arxiv.0805.1672,
title = {Universal Cycles of Discrete Functions},
author = {Britni LaBounty-Lay and Ashley Bechel and Anant P. Godbole},
journal= {arXiv preprint arXiv:0805.1672},
year = {2012}
}