#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 jmantysalo):
This got more speed with even very basic implementation of maximal chains
counting:
{{{
def countmax(P):
L = P.level_sets()
c = {}
for l in L[0]:
c[l] = 1
for lev in L[1:]:
for l in lev:
c[l] = sum(c[i] for i in P.lower_covers(l))
return sum(c[i] for i in P.maximal_elements())
}}}
If we have better way to make a order ideals lattice, it is a place for
new ticket. It would be nice feature in itself.
Hmm... Assuming we have `n`-element poset `P` and corresponding `L=J(P)`,
how we modify `L` when we add element `n+1` as a minimal element to `P`? I
guess the algorithm should be done by thinking this.
--
Ticket URL: <https://trac.sagemath.org/ticket/14126#comment:35>
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