2000 character limit reached
Signaletic operads (1906.02228v2)
Published 5 Jun 2019 in math.CO
Abstract: 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.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Collections
Sign up for free to add this paper to one or more collections.