#14126: Count Number of Linear Extensions of a Poset
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Reporter: csar | Owner: sage-combinat
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: combinatorics | Resolution:
Keywords: days45 | Merged in:
Authors: Jori Mäntysalo | Reviewers:
Report Upstream: N/A | Work issues:
Branch: u/jmantysalo | Commit:
/count-lin-ext | f908696aa7c63cefbc382af326cfe085e0dfa522
Dependencies: | Stopgaps:
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Comment (by kdilks):
Whatever it is, asymptotics aren't particularly relevant when in practice
we're not going past |P|>100.
Even without any wizardry,
{{{P.order_ideals_lattice().chain_polynomial().leading_coefficient()}}}
(the naive implementation I mentioned) is significantly faster than
{{{P.linear_extensions().cardinality()}}} (which defaults to using the
iterator and generates all of them). Twice as fast on the antichain of 8
elements, ten times as fast on {{{P=Posets.TamariLattice(4)}}} (14
elements, 20243 linear extensions), ~600 times as fast on
{{{P=Posets.IntegerCompositions(5)}}} (16 elements, 1680384 linear
extensions).
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Ticket URL: <https://trac.sagemath.org/ticket/14126#comment:33>
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