P' = dual P
The dual of a poset is the poset on the same ground set but with all relations reversed.
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Clearly then, the chain posets and booleanLattices are all self-dual.
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The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/Posets.m2:2635:0.