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Abstract:

We define a partial order on the set of faces of the permutohedron, which extends the weak Bruhat order of the symmetric group. The restriction of this order gives a partially ordered set structure to the set of faces of the associahedron, which extends the Tamari order defined on the set of planar binary rooted trees. These orders are used to describe associative algebra structures on the vector spaces spanned by the set of faces of the permutohedra on one hand, and on the vector space spanned by the set of planar rooted trees on the other hand. Our results extend the description of the dendriform algebra structure on the spaces spanned by permutations and by planar binary trees in terms of the weak Bruhat order and the Tamari order, respectively, obtained by J.-L. Loday and the second author in [J.-L. Loday, M. Ronco, Order structure and the algebra of permutations and of planar binary trees, J. Algebraic Combin. 15 (2002) 253-270]. © 2005 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:Weak Bruhat order on the set of faces of the permutohedron and the associahedron
Autor:Palacios, P.; Ronco, M.O.
Filiación:Departamento de Matemáticas, FCEN, Universidad de Buenos Aires, Pab. I, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Departamento de Matemática, Facultad de Ciencias, Universidad de Valparaíso, Avda. Gran Bretaña, 1091 Valparaíso, Chile
Año:2006
Volumen:299
Número:2
Página de inicio:648
Página de fin:678
DOI: http://dx.doi.org/10.1016/j.jalgebra.2005.09.042
Handle:http://hdl.handle.net/20.500.12110/paper_00218693_v299_n2_p648_Palacios
Título revista:Journal of Algebra
Título revista abreviado:J. Algebra
ISSN:00218693
CODEN:JALGA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00218693_v299_n2_p648_Palacios.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v299_n2_p648_Palacios

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Citas:

---------- APA ----------
Palacios, P. & Ronco, M.O. (2006) . Weak Bruhat order on the set of faces of the permutohedron and the associahedron. Journal of Algebra, 299(2), 648-678.
http://dx.doi.org/10.1016/j.jalgebra.2005.09.042
---------- CHICAGO ----------
Palacios, P., Ronco, M.O. "Weak Bruhat order on the set of faces of the permutohedron and the associahedron" . Journal of Algebra 299, no. 2 (2006) : 648-678.
http://dx.doi.org/10.1016/j.jalgebra.2005.09.042
---------- MLA ----------
Palacios, P., Ronco, M.O. "Weak Bruhat order on the set of faces of the permutohedron and the associahedron" . Journal of Algebra, vol. 299, no. 2, 2006, pp. 648-678.
http://dx.doi.org/10.1016/j.jalgebra.2005.09.042
---------- VANCOUVER ----------
Palacios, P., Ronco, M.O. Weak Bruhat order on the set of faces of the permutohedron and the associahedron. J. Algebra. 2006;299(2):648-678.
http://dx.doi.org/10.1016/j.jalgebra.2005.09.042