Chapoton, Frédéric Opérades différentielles graduées sur les simplexes et les permutoèdres. (Differential graded operads related to simplices and permutohedra). (French) Zbl 1044.18007 Bull. Soc. Math. Fr. 130, No. 2, 233-251 (2002). The author defines several differential graded operads. These are related to families of polytopes. For the family \(\Pi\), the underlying complexes are cellular cochains of permutohedra, and for the family {Pasc} the underlying complexes are chains of standard simplices. Generators and relations presentations are given for these operads, for the operad \(K\) associated with associahedra [F. Chapoton, Trans. Am. Math. Soc. 354, 63–74 (2002; Zbl 1035.18006)], and for their duals. The matter in this paper completes nicely a diagram of operads that were introduced by J.-L. Loday [Lect. Notes Math. 1763, 7–66 (2001; Zbl 0999.17002)]. Reviewer: Christian Blanchet (Vannes) Cited in 1 ReviewCited in 11 Documents MSC: 18D50 Operads (MSC2010) 52B11 \(n\)-dimensional polytopes 17A32 Leibniz algebras 17D25 Lie-admissible algebras Keywords:operads; simplices; permutohedra; associahedra; pre-Lie algebra; differential graded algebra; dendriform Citations:Zbl 1035.18006; Zbl 0999.17002 PDFBibTeX XMLCite \textit{F. Chapoton}, Bull. Soc. Math. Fr. 130, No. 2, 233--251 (2002; Zbl 1044.18007) Full Text: DOI Link