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### Find certain subposets of lattices

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.

### Find certain subposets of lattices

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.

### Find certain subposets of lattices

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.