Signed permutations and the four color theorem

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To each permutation $σ$ in $S_{n}$ we associate a triangulation of a fixed $(n+2)$-gon. We then determine the fibers of this association and show that they coincide with the sylvester classes depicted By Novelli, Hivert and Thibon. A signed version of this construction allows us to reformulate the four color theorem in terms of the existence of a signable path between any two permutations in the Cayley graph of the symmetric group $S_{n}.
29 pages, 9 figures

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Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/114076

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0606726
 http://arxiv.org/abs/math/0606726

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arXiv