### Abstract

A universal cycle for permutations of length n is a cyclic word or permutation, any factor of which is order-isomorphic to exactly one permutation of length n, and containing all permutations of length n as factors. It is well known that universal cycles for permutations of length n exist. However, all known ways to construct such cycles are rather complicated. For example, in the original paper establishing the existence of the universal cycles, constructing such a cycle involves finding an Eulerian cycle in a certain graph and then dealing with partially ordered sets. In this paper, we offer a simple way to generate a universal cycle for permutations of length n, which is based on applying a greedy algorithm to a permutation of length n - 1. We prove that this approach gives a unique universal cycle In for permutations, and we study properties of I
_{n} .

Original language | English |
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Pages (from-to) | 61-72 |

Number of pages | 12 |

Journal | International Journal of Foundations of Computer Science |

Volume | 30 |

Issue number | 1 |

DOIs | |

Publication status | Published - 5 Mar 2019 |

### Keywords

- universal cycles
- permutations
- greedy algorithm
- combinatorial generation

## Profiles

## Cite this

*International Journal of Foundations of Computer Science*,

*30*(1), 61-72. https://doi.org/10.1142/S0129054119400033