Year: 2025
Type: article
Abstract: 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 $$m=1$$ m = 1 , our Hochschild polytope is a deformed permutahedron whose oriented skeleton is the Hasse diagram of the Hochschild lattice.
Source: Mathematische Annalen
Authors: Vincent Pilaud, Daria Poliakova
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Awards: G2262748287, Beyond Permutahedra and Associahedra, G2766336479, G3005324705, G3480869486, G425668148, G492230693, G5984115212, G6325762137, G7013227978, G7084143925, Beyond Permutahedra and Associahedra: Geometry, Combinatorics, Algebra, and Probability, G84477964, Clusters, Homological Algebra, Representations and Mirror Symmetry
OpenAlex ID: W4409622922