#12930: Poset of Alternating sign matrices
-------------------------------------------------------------+--------------
Reporter: aschilling | Owner:
sage-combinat
Type: enhancement | Status:
needs_review
Priority: major | Milestone:
sage-5.4
Component: combinatorics | Resolution:
Keywords: alternating sign matrices, posets, days38 | Work issues:
Report Upstream: N/A | Reviewers:
Frédéric Chapoton, Anne Schilling
Authors: Pierre Cagne | Merged in:
Dependencies: | Stopgaps:
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Changes (by chapoton):
* status: needs_work => needs_review
Old description:
> Implementation of the poset of alternating sign matrices
>
> This is best done by implementing a bijection to monotone triangles (or
> contre tableaux). This was already done in MuPAD
>
> http://mupad-combinat.svn.sourceforge.net/viewvc/mupad-combinat/trunk
> /MuPAD-Combinat/lib/COMBINAT/alternatingSignMatrices.mu?view=log
>
> One way of the bijection is already implemented::
>
> {{{
> sage: import sage.combinat.alternating_sign_matrix as asm
> sage: asm.from_contre_tableau([[1, 2, 3], [1, 2], [1]])
> [0 0 1]
> [0 1 0]
> [1 0 0]
> sage: asm.from_contre_tableau([[1, 2, 3], [2, 3], [3]])
> [1 0 0]
> [0 1 0]
> [0 0 1]
> }}}
>
> It remains to implement the reverse bijection, and the ASM lattice from
> the ContreTableaux lattice.
>
> Apply [attachment:trac_12930-add_mt_lattice-as.patch]
New description:
Implementation of the poset of alternating sign matrices
This is best done by implementing a bijection to monotone triangles (or
contre tableaux). This was already done in MuPAD
http://mupad-combinat.svn.sourceforge.net/viewvc/mupad-combinat/trunk
/MuPAD-Combinat/lib/COMBINAT/alternatingSignMatrices.mu?view=log
One way of the bijection is already implemented::
{{{
sage: import sage.combinat.alternating_sign_matrix as asm
sage: asm.from_contre_tableau([[1, 2, 3], [1, 2], [1]])
[0 0 1]
[0 1 0]
[1 0 0]
sage: asm.from_contre_tableau([[1, 2, 3], [2, 3], [3]])
[1 0 0]
[0 1 0]
[0 0 1]
}}}
It remains to implement the reverse bijection, and the ASM lattice from
the ContreTableaux lattice.
Apply [attachment:trac_12930-add_mt_lattice-v2.patch]
--
Comment:
apply only trac_12930-add_mt_lattice-v2.patch
I have added deprecations, but I am not sure that I have done it right.
Could you please check ? Is it necessary to deprecate every single method
in the classes of contre-tableaux ? I have not done that.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12930#comment:22>
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