# Saturated chains

I know there is a command to take all maximal chains and all cover relations of a poset. I am working with a ranked poset and I am wondering if there is a command for all saturated chains in a poset. I appreciate any help given.

This is not my field so I can ask a silly question: Is every saturated chain a subchain of a maximal chain?

See also Stack Overflow question 52105780.

Yes. Every saturated chain is a maximal chain of a subposet.

My naive idea was to take all subchains of all maximal chains. This works, but it is inefficient because you get duplicates.