Abstract: The Hochschild lattice arises from a particular acyclic orientation of the "freehedron", a certain truncation of the hypercube introduced by Saneblidze in the context of a Hochschild complex connected to the free loop fibration. This lattice has remarkable combinatorial properties, and can be realized as a poset of integer tuples under componentwise order.
We prove that the ground set of the Hochschild lattice can be reordered in a canonical way such that the resulting order recovers a certain family of Greene's shuffle lattices.  Moreover, we establish an enumerative connection between the Hochschild lattice and its corresponding shuffle lattice based on the f- and h-vector of the freehedron.
We explain in which sense the relationship between the freehedron, the Hochschild lattice and the corresponding shuffle lattice is analogous to the well-known connection between the associahedron, the Tamari lattice and the noncrossing partition lattice.

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Meeting-ID: 937 7834 3609
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