Decomposing simple permutations, with enumerative consequences
Combinatorics
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0606186,
title = {Decomposing simple permutations, with enumerative consequences},
author = {Robert Brignall and Sophie Huczynska and Vince Vatter},
journal= {arXiv preprint arXiv:math/0606186},
year = {2007}
}