#10817: implementation of the generalized associahedron as a polyhedral complex
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Reporter: stumpc5 | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone:
Component: combinatorics | Keywords: associahedra
Author: Christian Stump | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Description changed by stumpc5:
Old description:
> The patch contains the implementation of the generalized associahedron,
> as constructed in Chapoton, Fomin, Zelevinsky - Polytopal realizations of
> the generalized associahedra, http://arxiv.org/abs/math/0202004.
>
> {{{
> sage: Associahedron(['A',3])
> Generalized associahedron of type ['A', 3] with 14 vertices
> }}}
>
> The class inherits from Polyhedra, and uses several new methods for root
> spaces.
New description:
The patch contains the implementation of the generalized associahedron, as
constructed in [CFZ] Chapoton, Fomin, Zelevinsky - Polytopal realizations
of the generalized associahedra, http://arxiv.org/abs/math/0202004.
{{{
sage: Associahedron(['A',3])
Generalized associahedron of type ['A', 3] with 14 vertices
}}}
The class inherits from Polyhedra, and uses several new methods for root
spaces:
- `RootLatticeRealization`.index_bipartition, returns the bipartition of
the indices of the Dynkin diagram vertices, if it is bipartite
- `RootLatticeRealization`.almost_positive_roots, returns the sorted list
of positive and simple negative roots
- `RootLatticeRealization`.tau_plus_minus, returns two piecewise linear
operators on the root space which are used to define the "tropical Coxeter
element" in [CFZ]
- `RootLatticeRealization`.almost_positive_root_decomposition, returns the
orbit decomposition of the almost positive roots under the dihedral group
action of < tau_plus, tau_minus > as defined above
Some documentation is still missing!
--
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10817#comment:2>
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