Order Structure on the Algebra of Permutations and of Planar Binary Trees |
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| Authors: | Jean-Louis Loday María O Ronco |
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| Institution: | (1) Institut de Recherche Mathématique Avancée, CNRS et Université, Louis Pasteur 7 rue R. Descartes, 67084 Strasbourg Cedex, France;(2) Departamento de Matemática, Ciclo Básico Común, Universidad de Buenos Aires, Pab. 3, Ciudad Universitaria, Nuñez, (, 1428 Buenos-Aires, Argentina |
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| Abstract: | Let X
n 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 0
KX
n]. We prove that it can be described explicitly by using the weak Bruhat order on S
n, the left-to-right order on planar trees, the lexicographic order in the cube case. |
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| Keywords: | planar binary tree order structure weak Bruhat order algebra of permutations dendriform algebra |
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