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Homological freeness criterion for operadic modules and application to Cohen-Macalayness of posets
Paul Laubie
We show a variation of the usual homological freeness criterion for operadic modules over a Koszul operad. We then apply this result to decorated partition posets for some operads,…
On Hilbert series of Koszul operads and a classification result for set-operads
Paul Laubie
Motivated by numerous examples in the literature, we state a conjecture on the Hilbert series of Koszul symmetric operads generated by one element of arity . We prove this conje…
Hypertrees and embedding of the operad
Paul Laubie
The operad encodes the algebraic structure on vector fields of Frobenius manifolds, in the same way as the operad encodes the algebraic structure on…
Combinatorics of pre-Lie products sharing a Lie bracket
Paul Laubie
We study in detail the operad controlling several pre-Lie algebra structures sharing the same Lie bracket. Specifically, we show that this operad admits a combinatorial description…