<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</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 free LAnKe on $3n-2$ generators: a theorem of Friedmann, Hanlon, Stanley and Wachs</style></title><secondary-title><style face="normal" font="default" size="100%">Electronic Journal Combinatorics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2026</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i2p23</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">33</style></volume><pages><style face="normal" font="default" size="100%">P2,23</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">A LAnKe (also known as a Filippov algebra or a Lie algebra of the n-th kind) is a vector space equipped with a skew-symmetric n-linear form that satisfies the generalized Jacobi identity. Friedmann, Hanlon, Stanley and Wachs have shown that the symmetric group acts on the multilinear part of the free LAnKe on 2n-1 generators as an irreducible representation. They announced that the multilinear component on 3n-2 generators decomposes as a direct sum of two irreducible symmetric group representations and a proof was given recently in a subsequent paper by Friedmann, Hanlon and Wachs. In the present paper we provide a proof of the later statement. The two proofs are substantially different.</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue></record></records></xml>