Signed permutations and the four color theorem [article]

Shalom Eliahou, Cedric Lecouvey
<span title="2006-06-28">2006</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="">arXiv:math/0606726v1</a> <a target="_blank" rel="external noopener" href="">fatcat:ul4hyxijunhb7hi3znjzkeawi4</a> </span>
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