Séminaire Lotharingien de Combinatoire, 91B.1 (2024), 12 pp.
Vincent Pilaud and Daria Poliakova
Hochschild Polytopes
Abstract.
The (m,n)-multiplihedron is a polytope whose faces correspond to
m-painted n-trees.
Deleting certain inequalities from its facet description, we obtain
the (m,n)-Hochschild polytope whose faces correspond to m-lighted
n-shades.
Moreover, there is a natural shadow map from m-painted n-trees to
m-lighted n-shades, which defines a meet semilattice morphism of
rotation lattices.
In particular, when m=1, our Hochschild polytope is a deformed
permutahedron realizing the Hochschild lattice.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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