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The [[order dimension]] of a partial order is the minimum cardinality of a set of linear extensions whose intersection is the given partial order; equivalently, it is the minimum number of linear extensions needed to ensure that each [[Critical pair (order theory)|critical pair]] of the partial order is reversed in at least one of the extensions.
[[Antimatroid]]s may be viewed as generalizing partial orders; in this view, the structures corresponding to the linear extensions of a partial order are the basic words of the antimatroid.<ref>{{citation
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