Let Sn be the symmetric group of all permutations of n letters, and let Sn(T) be the set of those permutations which avoid a given set of patterns T. In the present paper, we consider a τ-reduction argument where τ∈ Sm is given and all patterns in T are assumed to contain τ. For these situations, cell decompositions are introduced and studied. We describe an observation which allows to reduce the determination of the generating function for | Sn(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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- Pattern avoidance
ASJC Scopus subject areas
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics