Signaletic operads

Florent Hivert (1) , Vincent Pilaud (2, 3)

1 LRI - Laboratoire de Recherche en Informatique
2 CNRS - Centre National de la Recherche Scientifique
3 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

We introduce $k$-signaletic operads and their Koszul duals, generalizing the dendriform, diassociative and duplicial operads (which correspond to the $k=1$ case). We show that the Koszul duals of the $k$-signaletic operads act on multipermutations and that the resulting algebras are free, thus providing combinatorial models for these operads. Finally, motivated by these actions on multipermutations, we introduce similar operations on multiposets which yield yet another relevant operad obtained as Manin powers of the $L$-operad.

Domaines: Combinatoire [math.CO]

Florent Hivert, Vincent Pilaud. Signaletic operads. 2019. ⟨hal-02997608⟩