Geodesic
The Möbius function of separable permutations (extended abstract)
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010).

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A permutation is separable if it can be generated from the permutation 1 by successive sums and skew sums or, equivalently, if it avoids the patterns 2413 and 3142. Using the notion of separating tree, we give a computationally efficient formula for the Möbius function of an interval $(q,p)$ in the poset of separable permutations ordered by pattern containment. A consequence of the formula is that the Möbius function of such an interval $(q,p)$ is bounded by the number of occurrences of $q$ as a pattern in $p$. The formula also implies that for any separable permutation $p$ the Möbius function of $(1,p)$ is either 0, 1 or -1. 
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     author = {Jel{\'\i}nek, V{\'\i}t and Jel{\'\i}nkov\'a, Eva and Steingr{\'\i}msson, Einar},
     title = {The {M\"obius} function of separable permutations (extended abstract)},
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Jelínek, Vít; Jelínková, Eva; Steingrímsson, Einar. The Möbius function of separable permutations (extended abstract). Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010). doi : 10.46298/dmtcs.2805. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2805/

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