#12930: Poset of Alternating sign matrices
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Reporter: aschilling | Owner: sage-combinat
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.1
Component: combinatorics | Keywords: alternating sign matrices,
posets
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: |
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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.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12930>
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