1. Signaletic operads
- Author
-
Hivert, Florent, Pilaud, Vincent, Laboratoire de Recherche en Informatique (LRI), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS), Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), ANR-15-CE40-0004,SC3A,Surfaces, Catégorification et Combinatoire des Algèbres Amassées(2015), ANR-17-CE40-0018,CAPPS,Analyse Combinatoire de Polytopes et de Subdivisions Polyédrales(2017), Pilaud, Vincent, Surfaces, Catégorification et Combinatoire des Algèbres Amassées - - SC3A2015 - ANR-15-CE40-0004 - AAPG2015 - VALID, and Analyse Combinatoire de Polytopes et de Subdivisions Polyédrales - - CAPPS2017 - ANR-17-CE40-0018 - AAPG2017 - VALID
- Subjects
Shuffle product splitting ,Koszul duality ,dendriform algebras ,Mathematics::Algebraic Topology ,operads ,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO] ,Mathematics::K-Theory and Homology ,Mathematics::Quantum Algebra ,Mathematics::Category Theory ,18D50, 16T30, 05E15, 05C05, 68Q42 ,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] ,FOS: Mathematics ,Mathematics - Combinatorics ,Combinatorics (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., Comment: 97 pages, 20 figures
- Published
- 2019