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="https://arxiv.org/abs/math/0606726v1">arXiv:math/0606726v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ul4hyxijunhb7hi3znjzkeawi4">fatcat:ul4hyxijunhb7hi3znjzkeawi4</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-math0606726/math0606726.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/04/81/0481d48d07cfe971fb9e5633a787fdd81244fa2f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0606726v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>