Signaletic operads
arXiv:1906.02228
Abstract
We introduce -signaletic operads and their Koszul duals, generalizing the dendriform, diassociative and duplicial operads (which correspond to the case). We show that the Koszul duals of the -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 -operad.
101 pages, 20 figures. Version 2: Many presentation improvements following referee advices