A New Upper Bound for 1324-Avoiding Permutations. (September 2014) - BÓNA, MIKLÓS; Broutin, Nicolas; Fill, James Allen; Nebel, Markus; Ward, Mark Daniel
<x content-type="archive" xml:space="preserve">Abstract</x> We prove that the number of 1324-avoiding permutations of length n is less than <alternatives><inline-graphic xlink:href="ark:/27927/pgh1238jc0n" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> <![CDATA[$(7+4\sqrt{3})^n$]]> </alternatives>. The novelty of our method is that we injectively encode such permutations by a pair of words of length n over a finite alphabet that avoid a given factor.