Obtaining integers from a linear extension of a poset.

joakim_uhlin
150 ●1 ●3 ●16

5311 ●4 ●44 ●118

I'm quite new to Sage so this might be a very easy question.

Suppose that I have defined a linear extension of a poset in Sage like this:

P = Poset(([1,2,3,4], [[1,3],[1,4],[2,3]]), linear_extension=True, facade=False)
p = P.linear_extension([1,4,2,3])

Is there a way for me to make this linear extension into a permutation? That is, I would like to obtain the permutation [1,4,2,3] from p.

1 Answer

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This is not my field, but it seems you can do

sage: map(lambda x: x.element, p)
[1, 4, 2, 3]
sage: sigma = Permutation(map(lambda x: x.element, p))
sage: sigma
[1, 4, 2, 3]
sage: sigma(2)
4

More pythonic:

sage: Permutation(x.element for x in p)
[1, 4, 2, 3]

Or just use facade=True

FrédéricC ( 2019-03-05 21:11:45 +0100 )edit

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Asked: 2019-03-05 16:21:13 +0100

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Last updated: Mar 05 '19