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hasse diagram of a subset of a poset

asked 2015-10-06 08:39:38 -0500

GA316 gravatar image

updated 2016-07-12 13:32:20 -0500

FrédéricC gravatar image

E = {1,2,3} P = SetPartitions(E) This gives the set of all partitions of E,. I have a subset Q of P and I want to construct the directed graph whose vertex set is this set Q and we draw an arrow from p to q in this graph if q covers p. How to construct this graph for a given P and Q?

The definition of covering relation can be found here : https://en.wikipedia.org/wiki/Coverin...

Thanks for your valuable timing.

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answered 2015-10-06 11:00:49 -0500

fidbc gravatar image

If you use your favorite search engine, you may come accross this site.

There you can see that

P = SetPartitions(3)
f = lambda q,p: q in p.refinements()
Po = Poset((P,f))

constructs the associated poset Po. Then you can simply use the subposet method together to get the desired subposet Q. Getting the Hasse diagram for Q is just a matter of using Q.show()

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it works nicely.thanks.

GA316 gravatar imageGA316 ( 2015-10-08 02:26:48 -0500 )edit

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Asked: 2015-10-06 08:39:38 -0500

Seen: 120 times

Last updated: Oct 06 '15