# Discrete Mathematics & Theoretical Computer Science

## Volume 6 n° 2 (2004), pp. 461-470

author: | Toufik Mansour |
---|---|

title: | On an open problem of Green and Losonczy: exact enumeration of freely braided permutations |

keywords: | restricted permutations, freely braided permutations, generating functions |

abstract: | Recently, Green and Losonczy GL1,GL2 introduced freely braided permutation as a special class of restricted permutations has arisen in representation theory. The freely braided
permutations were introduced and studied as the upper bound for
the number of commutation classes of reduced expressions for an
element of a simply laced Coxeter group is achieved if and only if
when the element is freely braided. In this paper, we prove that
the generating function for the number of freely braided
permutations in S is given by
_{n}
1-3x-2x
^{2}+(1+x)√1-4x
1-4x-x
^{2}+(1-x^{2})√1-4x
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reference: | Toufik Mansour (2004),
On an open problem of Green and Losonczy: exact enumeration of freely braided permutations,
Discrete Mathematics and Theoretical Computer Science 6, pp. 461-470 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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Automatically produced on Sun Nov 7 16:55:08 CET 2004 by falk