<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>12</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">M. Maliakas</style></author><author><style face="normal" font="default" size="100%">D.-D. Stergiopoulou</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On the action of the symmetric group on the free LAnKe: a question of Friedmann, Hanlon, Stanley and Wachs</style></title><secondary-title><style face="normal" font="default" size="100%">arXiv</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">Submitted</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/2410.06979</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;span&gt;&lt;span&gt; &lt;/span&gt;A LAnKe (also known as a Lie algebra of the th kind, or a Filippov algebra) is a vector space equipped with a skew-symmetric -linear form that satisfies the generalized Jacobi identity. The symmetric group&amp;nbsp; acts on the multilinear part of the free LAnKe on&amp;nbsp; generators, where&amp;nbsp; is the number of brackets, by permutation of the generators. The corresponding representation was studied by Friedmann, Hanlon, Stanley and Wachs, who asked whether for , its irreducible decomposition contains no summand whose Young diagram has at most&amp;nbsp; columns. The answer is affirmative if $k \le 3$. In this paper, we show that the answer is affirmative for all $k$&lt;/span&gt;</style></abstract><issue><style face="normal" font="default" size="100%">2410.06979</style></issue></record></records></xml>