### Abstract

Motivated by a new point of view to study occurrences of consecutive patterns in permutations, we introduce the notion of uniquely k-determined permutations. We give two criteria for a permutation to be uniquely k-determined: one in terms of the distance between two consecutive elements in a permutation, and the other one in terms of directed hamiltonian paths in the certain graphs called path-schemes. Moreover, we describe a finite set of prohibitions that gives the set of uniquely k-determined permutations. Those prohibitions make the application of the transfer matrix method possible for determining the number of uniquely k-determined permutations.

Original language | English |
---|---|

Pages (from-to) | 1500-1507 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 308 |

Issue number | 9 |

Early online date | 6 Apr 2007 |

DOIs | |

Publication status | Published - May 2008 |

### Keywords

- de Bruijn graph
- consecutive pattern
- set of prohibitions
- permutations
- reconstruction

## Fingerprint Dive into the research topics of 'On uniquely k-determined permutations'. Together they form a unique fingerprint.

## Cite this

Avgustinovich, S., & Kitaev, S. (2008). On uniquely k-determined permutations.

*Discrete Mathematics*,*308*(9), 1500-1507. https://doi.org/10.1016/j.disc.2007.03.079