Signed permutations and the four color theorem

Details Signed permutations and the four color theorem Signed permutations and the four color theorem

2006-06-28

arxiv.org/abs/math/0606726v1

Mathematics

Combinatorics

29 pages, 9 figures

Scientific paper

To each permutation $\sigma$ 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}.

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