Universal Cycles of Discrete Functions

Details Universal Cycles of Discrete Functions Universal Cycles of Discrete Functions

2008-05-12

arxiv.org/abs/0805.1672v1

Congressus Numerantium 189, 121-128, 2008

Mathematics

Combinatorics

Scientific paper

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 $U$-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.

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