Hochschild polytopes

The (m, n)-multiplihedron is a polytope whose faces correspond to m-painted n-trees, and whose oriented skeleton is the Hasse diagram of the rotation lattice on binary m-painted n-trees. Deleting certain inequalities from the facet description of the (m, n)-multiplihedron, we construct the (m, n)-Ho...

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Detalles Bibliográficos
Autores: Pilaud, Vincent, Poliakova, D.
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/484406
Acceso en línea:http://hdl.handle.net/2072/484406
Access Level:acceso abierto
Palabra clave:Polytopes
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Descripción
Sumario:The (m, n)-multiplihedron is a polytope whose faces correspond to m-painted n-trees, and whose oriented skeleton is the Hasse diagram of the rotation lattice on binary m-painted n-trees. Deleting certain inequalities from the facet description of the (m, n)-multiplihedron, we construct the (m, n)-Hochschild polytope whose faces correspond to m-lighted n-shades, and whose oriented skeleton is the Hasse diagram of the rotation lattice on unary m-lighted n-shades. Moreover, there is a natural shadow map from m-painted n-trees to m-lighted n-shades, which turns out to define a meet semilattice morphism of rotation lattices. In particular, when m=1, our Hochschild polytope is a deformed permutahedron whose oriented skeleton is the Hasse diagram of the Hochschild lattice.