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Obtaining certain minimal elements for lattices

asked 4 years ago

klaaa gravatar image

updated 4 years ago

Let L be a finite lattice and Lop the opposite lattice. We can then look at the product lattice U=Lop×L and inside U the poset SL= { (r1,r2)Lop×L|r2r1 }. My question is whether there is an easy way to obtain the poset SL for a given lattice L together with the minimal elements min(SL) of SL.

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answered 4 years ago

FrédéricC gravatar image

updated 4 years ago

Like this maybe

sage: L = posets.TamariLattice(2)
sage: U = L.dual() * L
sage: S = U.subposet((x,y) for x,y in U if not L.le(y,x))
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Thank you very much. My guess for general lattices was wrong, so I deleted it.

klaaa gravatar imageklaaa ( 4 years ago )

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Asked: 4 years ago

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Last updated: Oct 10 '20