#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: | 88b08d58b257dbaa72ab98f027cc5023d7224a2a
Frédéric Chapoton | Stopgaps:
Report Upstream: N/A |
Branch: |
u/chapoton/18347 |
Dependencies: |
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Comment (by chapoton):
Hello,
yes, this is a rather subtle order, I think. It is indeed closely related
to noncrossing
partitions and to the weak order, but not in obvious ways. For example,
the Mobius number is the number of connected partitions.
Concerning 4: I have added an option to specify the output of decreasing
runs. Should I do the same for runs ?
Concerning 5: I have added this as a simple necessary condition
concerning 6: I have made `shard_preorder_graph` input a tuple of pairs
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Ticket URL: <http://trac.sagemath.org/ticket/18347#comment:12>
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