Obtaining the poset of monotone functions

asked 2022-09-06 14:54:11 +0100

klaaa gravatar image

updated 2022-09-06 14:55:45 +0100

Let $P$ and $Q$ be finite posets. Is there an easy way to obtain the poset (with the natural order) of monotone function from P to Q via Sage? Is it possible to obtain also the poset of injective (or surjective) monotone functions?

Special cases would also be interesting such as when P and Q are lattices or total orders.

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There is P.intervals_poset() for a specific case.

FrédéricC gravatar imageFrédéricC ( 2022-09-07 11:56:03 +0100 )edit

Does Sage only provides a direct way to iterate over all nondecreasing (or monotone) maps between two finite posets ?

tmonteil gravatar imagetmonteil ( 2022-09-07 17:41:09 +0100 )edit