2023/07/12 by Vincent Pilaud, Daria Poliakova, Pilaud, Vincent +1 · 2 citations
Mathematics · #05A15 #05E99 #06B10 #52B11 #52B12 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research
paper · doi:10.48550/arxiv.2307.05940
openalex publication_date 2023/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.