Decomposing simple permutations, with enumerative consequences

Details Decomposing simple permutations, with enumerative consequences Decomposing simple permutations, with enumerative consequences

2006-06-08

arxiv.org/abs/math/0606186v1

Mathematics

Combinatorics

Scientific paper

We prove that every sufficiently long simple permutation contains two long almost disjoint simple subsequences. This result has applications to the enumeration of restricted permutations. For example, it immediately implies a result of Bona and (independently) Mansour and Vainshtein that for any r, the number of permutations with at most r copies of 132 has an algebraic generating function.

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