Toufik Mansour - On an open problem of Green and Losonczy: exact enumeration of freely braided permutations

dmtcs:327 - Discrete Mathematics & Theoretical Computer Science, January 1, 2004, Vol. 6 no. 2 - https://doi.org/10.46298/dmtcs.327
On an open problem of Green and Losonczy: exact enumeration of freely braided permutationsArticle

Authors: Toufik Mansour ORCID1

  • 1 Department of Mathematics [Haïfa]

Recently, Green and Losonczy~GL1,GL2 introduced \emphfreely 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_n is given by \par (1-3x-2x^2+(1+x)√1-4x) / (1-4x-x^2+(1-x^2)√1-4x).\par


Volume: Vol. 6 no. 2
Published on: January 1, 2004
Imported on: March 26, 2015
Keywords: restricted permutations,freely braided permutations,generating functions,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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