Abstract
Let \(\mathcal {S}_n\) be the symmetric group of all permutations of n letters, and let \(\mathcal {S}_n(T)\) be the set of those permutations which avoid a given set of patterns T. In the present paper, we consider a \(\tau \)-reduction argument where \(\tau \in \mathcal {S}_m\) is given and all patterns in T are assumed to contain \(\tau \). For these situations, cell decompositions are introduced and studied. We describe an observation which allows to reduce the determination of the generating function for \(|\mathcal {S}_n(T)|\) to the determination of a set of generating functions for simpler problems. The usefulness of this approach is demonstrated by several examples.
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This paper is part of the ACA 2017 Jerusalem Special Issue.
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Mansour, T., Schork, M. Permutation Patterns and Cell Decompositions. Math.Comput.Sci. 13, 169–183 (2019). https://doi.org/10.1007/s11786-018-0353-5
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DOI: https://doi.org/10.1007/s11786-018-0353-5