Algèbres de Hopf des permutahèdres, associahèdres et hypercubes

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Three graded Hopf algebras over ℤ are constructed, each one having in degree n a basis indexed by the faces of a polytope of dimension n-1, respectively, the hypercube, the associahedron, and the permutahedron. This lifts to the level of all faces previous constructions of Loday and Ronco and Malvenuto and Reutenauer for vertices of the same polyhedra. Copyright 2000 Academic Press.

Document Type: Research Article

Affiliations: Institut de Mathématiques, Université Pierre et Marie Curie, 4, Place Jussieu, Paris, 75005, France

Publication date: March 1, 2000

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