2019/06/06 by Daniel López, López, Daniel, Louis-François Préville-Ratelle +2
Mathematics · #05E05 #16T30 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1906.02834
openalex publication_date 2019/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a simplicial object (\ \Dym\m≥ 0, \mathbb Fi, \mathbb Sj) in the category of non-symmetric algebraic operads, satisfying that \Dy0 is the operad of associative algebras and \Dy1 is J.-L. Loday\rq s operad of dendriform algebras. The dimensions of the operad \Dym are given by the Fuss-Catalan numbers. Given a family of partially ordered sets \bold P=\Pn\n≥ 1 we show that, under certain conditions, the vector space spanned by the set of m-simpleces of \bold P is a \Dym algebra. This construction, applied to certain combinatorial Hopf algebras, whose associative product comes from a dendriform structure, provides examples of \Dym algebras.