Obtaining the subposet of dissectors of a poset

Poset

asked 2018-01-14 19:25:58 +0100

sagequstions
187 ●2 ●7 ●15

Following http://citeseerx.ist.psu.edu/viewdoc/... on page 3, the set of Dissectors Dis(P) of a poset P is defined as the subposet of P of elements x such that the order filter generated by x has a complement which is a principal order ideal. Is there an easy way to obtain this poset via Sage and calculate its width?

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answered 2018-01-15 14:57:35 +0100

FrédéricC

5206 ●3 ●43 ●114

updated 2018-01-15 14:57:49 +0100

Maybe like that

sage: P = posets.PentagonPoset()
sage: [u for u in P if len(P.panyushev_complement([u]))==1]
[1, 3]
sage: P.subposet([u for u in P if len(P.panyushev_complement([u]))==1])
Finite poset containing 2 elements

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Asked: 2018-01-14 19:25:58 +0100

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Last updated: Jan 15 '18

Obtaining the subposet of dissectors of a poset edit

1 Answer