Cellular diagonals of permutahedra (original) (raw)

2.1. Partition forests 2.2. Möbius polynomial 2.3. Rainbow forests 2.4. Enumeration of vertices of B ℓ n 2.5. Enumeration of regions and bounded regions of B ℓ n 3. Face poset and combinatorial description of B ℓ n (a) 3.1. Ordered partition forests 3.2. From partition forests to ordered partition forests 3.3. A criterion for ordered partition forests Part II. Diagonals of permutahedra 4. Cellular diagonals 4.1. Cellular diagonals for polytopes 4.2. Cellular diagonals for the permutahedra 4.3. Enumerative results on cellular diagonals of the permutahedra 5. Operadic diagonals 5.1. The LA and SU diagonals 5.2. The operadic property 5.3. Isomorphisms between operadic diagonals 5.4. Facets of operadic diagonals 5.5. Vertices of operadic diagonals 5.6. Relation to the facial weak order 6. Shift lattices 6.1. Topological enhancement of the original SU diagonal 6.2. Shifts under the face poset isomorphism 6.3. Shift lattices 6.4. Cubical description 6.5. Matrix description Part III. Higher algebraic structures 7. Higher tensor products 7.1. Topological operadic structures 7.2. Relating operadic structures 7.3. Tensor products References