#15683: Interval-posets of Tamari
-------------------------------------+-------------------------------------
Reporter: VivianePons | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.2
Component: combinatorics | Resolution:
Keywords: combinat, Tamari, | Merged in:
binary trees, Dyck paths | Reviewers:
Authors: Viviane Pons | Work issues:
Report Upstream: N/A | Commit:
Branch: public/combinat | 1d33146e3974ee718b618e0ea2f8494dae2aae90
/interval-posets-15683 | Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Comment (by VivianePons):
> I think we should merge #14498 into this branch, shouldn't we? I'm
referring to one of the methods from #14498 for its doc. (Namely, for the
definition of the Tamari order on trees. By the way, does that definition
play well with the one you are using?)
We should merge nly if there is a conflict.. Is there any? And if you're
asking if the definition of the Tamari order is the same: yes of course.
And I added a method on the binary tree class to get an interval-poset.
> I have revamped your references as they were too short and conflicting
with some existing ones ("Cha" is way too common for an identifier).
>
Thank you
> This is probably a stupid question a more careful look at the code would
answer, but where do I find a method to turn a Tamari interval-poset into
a poset? While you have redefined some poset-theoretical methods, there
are still many more in the Poset class.
This was no stupid question. The poset was stored in ``self._poset`` but I
have added a ``poset()`` method which makes it more visible.
>
> I've added an arXiv identifier to the Chapoton reference. If you are
aware of the paper being more up-to-date than the arXiv preprint, please
remove it again.
>
> If I remember correctly, the Tamari lattice projects onto the Bruhat
poset (one of the two, I never remember which); are there any methods for
this?
The ``linear_extensions`` method return permutations which are linear
extensions of the interval-poset. They form indeed an interval of the
right weak order. There are also the two methos ``max_linear_extention``
and ``min_linear_extention`` which return both ends of the right weak
order interval. Tell me if you think there should be more or better
documented methods.
--
Ticket URL: <http://trac.sagemath.org/ticket/15683#comment:19>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/groups/opt_out.
