Hochschild polytopes
Year: 2023
Type: conference-paper
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 $m=1$, our Hochschild polytope is a deformed permutahedron whose oriented skeleton is the Hasse diagram of the Hochschild lattice.
Authors: Pilaud, Vincent, Poliakova, Daria
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2262748287, Beyond Permutahedra and Associahedra, G3005324705, G3010527862, G3480869486, G425668148, G4526231891, G4532494212, G5984115212, G6910422418, G7013227978, G7084143925, G7304226585, Beyond Permutahedra and Associahedra: Geometry, Combinatorics, Algebra, and Probability, Clusters, Homological Algebra, Representations and Mirror Symmetry
OpenAlex ID: W4384264693