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The Möbius function of separable permutations (extended abstract)
Discrete Mathematics & Theoretical Computer Science
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 $q$ asdoi:10.46298/dmtcs.2805 fatcat:7ouwvbpffvgjfoykicg3lkqf34