2019/06/05 by Florent Hivert, Vincent Pilaud, Hivert, Florent +1
Mathematics · #05C05 #05E15 #16T30 #18D50 #68Q42 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1906.02228
openalex publication_date 2019/06/05 · openalex created_date 2022/12/03 · openalex updated_date 2026/07/28
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.