Signed permutations and the four color theorem
Abstract
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}.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606726
 Bibcode:
 2006math......6726E
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 29 pages, 9 figures