@article {44056,
	title = {On the action of the symmetric group on the free LAnKe: a question of Friedmann, Hanlon, Stanley and Wachs},
	journal = {arXiv},
	year = {Submitted},
	abstract = {<span><span> </span>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\&nbsp; acts on the multilinear part of the free LAnKe on\&nbsp; generators, where\&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\&nbsp; columns. The answer is affirmative if $k \le 3$. In this paper, we show that the answer is affirmative for all $k$</span>},
	url = {https://arxiv.org/abs/2410.06979},
	author = {M. Maliakas and D.-D. Stergiopoulou}
}
