### Abstract

Language | English |
---|---|

Article number | P146 |

Number of pages | 12 |

Journal | The Electronic Journal of Combinatorics |

Volume | 18 |

Issue number | 1 |

Publication status | Published - 2011 |

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### Keywords

- consecutive pattern poset
- Möbius function

### Cite this

*The Electronic Journal of Combinatorics*,

*18*(1), [P146].

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*The Electronic Journal of Combinatorics*, vol. 18, no. 1, P146.

**The Möbius function of the consecutive pattern poset.** / Bernini, A.; Ferrari, L.; Steingrimsson, E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The Möbius function of the consecutive pattern poset

AU - Bernini, A.

AU - Ferrari, L.

AU - Steingrimsson, E.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - consecutive pattern poset

KW - Möbius function

UR - http://www.combinatorics.org/ojs/index.php/eljc/article/view/v18i1p146/pdf

UR - http://arxiv.org/abs/1103.0173

M3 - Article

VL - 18

JO - The Electronic Journal of Combinatorics

T2 - The Electronic Journal of Combinatorics

JF - The Electronic Journal of Combinatorics

SN - 1077-8926

IS - 1

M1 - P146

ER -