Geodesic
The Möbius function of the consecutive pattern poset
The electronic journal of combinatorics, Tome 18 (2011) no. 1

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Zbl arXiv EuDML
An occurrence of a consecutive permutation pattern $p$ in a permutation $\pi$ is a segment of consecutive letters of $\pi$ 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 $1$.
DOI : 10.37236/633
Classification : 05A05, 06A07
Mots-clés : consecutive permutation pattern, polynomial time algorithm 
Antonio Bernini; Luca Ferrari; Einar Steingrímsson. The Möbius function of the consecutive pattern poset. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/633
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     title = {The {M\"obius} function of the consecutive pattern poset},
     journal = {The electronic journal of combinatorics},
     year = {2011},
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     number = {1},
     doi = {10.37236/633},
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