#18347: implement the shard intersection order on permutations
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Reporter: | Owner:
chapoton | Status: needs_work
Type: | Milestone: sage-6.7
enhancement | Resolution:
Priority: minor | Merged in:
Component: | Reviewers:
combinatorics | Work issues:
Keywords: poset | Commit:
Authors: | e32ecc3a9702cc7ab69ba180eb75f02623418186
Frédéric Chapoton | Stopgaps:
Report Upstream: N/A |
Branch: |
u/chapoton/18347 |
Dependencies: |
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Comment (by vdelecroix):
Replying to [comment:8 chapoton]:
> Thanks for the comments. I have corrected the two minor ones.
>
> About the caching: indeed, this is used only in the poset, but used many
times.
It is currently not used '''in''' the poset, only during its construction!
Just have a look at the ugly poset code. It is not lazy at all.
4. `runs` and `decreasing_runs` should return the same data. It is
currently list for one of them and tuple for the other.
5. Why did you wrote the following comment in `shard_compares`?
{{{
# We assume that r1 has less runs than r0
}}}
6. The function `shard_preorder_graph` only depends on the interval not on
the runs themselves. So you are storing too much in the cache of this
function. Make the input a tuple of pairs
{{{
sage: s = Permutation([2,8,3,9,6,4,5,1,7])
sage: runs = s.decreasing_runs()
sage: shard_preorder_graph(runs) == \
....: shard_preorder_graph(tuple((r[0],r[-1]) for r in runs))
True
}}}
And you should really think moving it somewhere else as this has nothing
to do with permutations. This is just a comparability graph given by the
inclusion order on intervals. Isn't it?
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/18347#comment:9>
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