### 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 ¯nite 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.

prohibitions make the application of the transfer matrix method possible for determining the number of uniquely k-determined permutations.

Original language | English |
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Number of pages | 7 |

Publication status | Published - Jul 2007 |

Event | 19th International Conference on Formal Power Series & Algebraic Combinatorics - Nankai University, Tianjin, China Duration: 2 Jul 2007 → 6 Jul 2007 |

### Conference

Conference | 19th International Conference on Formal Power Series & Algebraic Combinatorics |
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Abbreviated title | FPSAC'07 |

Country | China |

City | Tianjin |

Period | 2/07/07 → 6/07/07 |

### Keywords

- k-determined permutations
- consecutive patterns
- permutations
- graphs

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## Cite this

Avgustinovich, S., & Kitaev, S. (2007).

*On uniquely k-determined permutations*. Poster session presented at 19th International Conference on Formal Power Series & Algebraic Combinatorics, Tianjin, China.