Universal Cycles of Discrete Functions

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 $U$-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.

Cited by in corpus (3)

• Universal Cycles of Restricted Classes of Words
• On Universal Cycles for new Classes of Combinatorial Structures
• Universal Cycles of Complementary Classes