### Abstract

An occurrence of a consecutive permutation pattern p in a permutation π is a segment of consecutive letters of π whose values appear in the same order of size as the letters in p. The set of all permutations forms a poset with respect to such pattern containment. We compute the Möbius function of intervals in this poset. For most intervals our results give an immediate answer to the question. In the remaining cases, we give a polynomial time algorithm to compute the Möbius function. In particular, we show that the Möbius function only takes the values −1, 0 and 1.

Original language | English |
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Article number | P146 |

Number of pages | 12 |

Journal | The Electronic Journal of Combinatorics |

Volume | 18 |

Issue number | 1 |

Publication status | Published - 2011 |

### Keywords

- consecutive pattern poset
- Möbius function

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## Cite this

Bernini, A., Ferrari, L., & Steingrimsson, E. (2011). The Möbius function of the consecutive pattern poset.

*The Electronic Journal of Combinatorics*,*18*(1), [P146].