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The set of permutations on ''n'' items can be given the structure of a [[partial order]], called the '''weak order of permutations''', which forms a [[lattice (order)|lattice]].
The [[Hasse_diagram|Hasse diagram]] of the inversion sets ordered by the [[subset]] relation forms the [[skeleton (topology)|skeleton]] of a [[permutohedron]].
If a permutation is assigned to each inversion set using the place-based definition, the resulting order of permutations is that of the permutohedron, where an edge corresponds to the swapping of two elements with consecutive values. This is the weak order of permutations. The identity is its minimum, and the permutation formed by reversing the identity is its maximum.
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