A New Upper Bound for 1324-Avoiding Permutations. (September 2014)

• Record Type: Journal Article
• Authors: BÓNA, MIKLÓS; Broutin, Nicolas; Fill, James Allen; Nebel, Markus; Ward, Mark Daniel
• Is Part Of: Combinatorics, probability and computing. Volume 23:Number 5(2014:Sep.)
• Page Start: 717
• Page End: 724
• Publication Date: 2014-09
• Subjects: Combinatorial analysis -- Periodicals; Probabilities -- Periodicals; Computer science -- Mathematics -- Periodicals; 511.6
• DOI: 10.1017/S0963548314000091
• Languages: English
• ISSNs: 0963-5483

Abstract

<abstract abstract-type="normal"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>We prove that the number of 1324-avoiding permutations of length <italic>n</italic> is less than <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh1238jc0n" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$(7+4\sqrt{3})^n$]]></tex-math></alternatives></inline-formula>. The novelty of our method is that we injectively encode such permutations by a pair of words of length <italic>n</italic> over a finite alphabet that avoid a given factor.</p> </abstract>