Equivalence class universal cycles for permutations
The paper sets out to construct a complete family of universal cycles of \(n\)-permutations using \(n+ 1\) symbols, and an equivalence relation based on differences. The notion of universal cycles as cyclic representations of combinatorial objects, a generalization of de Bruijn cycles, is of recent (1990's) interest---and the universal cycles for permutations examined in this paper is an example of this. Having set up the equivalence classes, the authors then construct a directed graph---which proves to be Eulerian. An Eulerian cycle provides the desired universal cycle for their example.
scientific article; zbMATH DE number 858106