Abstract
We study the values of the Möbius function μ of intervals in the containment poset of permutations. We construct a sequence of permutations πn of size 2n−2 for which μ(1,πn) is given by a polynomial in n of degree 7. This construction provides the fastest known growth of |μ(1,π)| in terms of |π|, improving a previous quadratic bound by Smith.Our approach is based on a formula expressing the Möbius function of an arbitrary permutation interval [α,β] in terms of the number of embeddings of the elements of the interval into β.
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