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

  • Authors:

  • Jean-Louis Loday;María O. Ronco

  • Affiliations:

  • Institut de Recherche Mathématique Avancée, CNRS et Université Louis Pasteur 7 rue R. Descartes, 67084 Strasbourg Cedex, France. loday@math.u-strasbg.fr;Departamento de Matemática, Ciclo Básico Común, Universidad de Buenos Aires Pab. 3, Ciudad Universitaria, Nuñez, (1428) Buenos-Aires, Argentina.mronco@mate.dm.uba.ar

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2002

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Abstract

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