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Let L be a given finite distributive lattice. I wonder whether there is a quick method to obtain the list of all subposets P of L having the following properties:
a) P is not a lattice.
b) L is the smallest lattice that contains P.
c) P is bounded (meaning it has a unique global maximum and a unique global minimum).
Thank you for any help.
Let L be a given finite distributive lattice. I wonder whether there is a quick method to obtain the list of all subposets P of L having the following properties:
a) P is not a lattice.
b) L is the smallest lattice that contains P.
c) P is bounded (meaning it has a unique global maximum and a unique global minimum).
Thank you for any help.
example: The distributive lattice L of alternating sign matrices contains the strong Bruhat order P of the symmetric group in that way.
Let L be a given finite distributive lattice. I wonder whether there is a quick method to obtain the list of all subposets P of L having the following properties:
a) P is not a lattice.
b) L is the smallest lattice that contains P.
c) P is bounded (meaning it has a unique global maximum and a unique global minimum).
Thank you for any help.
example: The distributive lattice L of alternating sign matrices contains the strong Bruhat order P of the symmetric group in that way.
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