Journal of Algebraic Combinatorics

, Volume 15, Issue 3, pp 253–270 | Cite as

Order Structure on the Algebra of Permutations and of Planar Binary Trees

  • Jean-Louis Loday
  • María O. Ronco


Let Xn be either the symmetric group on n letters, the set of planar binary n-trees or the set of vertices of the (n − 1)-dimensional cube. In each case there exists a graded associative product on ⊕n≥0K[Xn]. We prove that it can be described explicitly by using the weak Bruhat order on Sn, the left-to-right order on planar trees, the lexicographic order in the cube case.

planar binary tree order structure weak Bruhat order algebra of permutations dendriform algebra 


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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Jean-Louis Loday
    • 1
  • María O. Ronco
    • 2
  1. 1.Institut de Recherche Mathématique AvancéeCNRS et UniversitéStrasbourg CedexFrance
  2. 2.Departamento de Matemática, Ciclo Básico ComúnUniversidad de Buenos AiresBuenos-AiresArgentina

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