#7492: Decomposition of a doubly stochastic matrix as a convex sum of
permutations
(Birkhoff–von Neumann Theorem)
-----------------------------+----------------------------------------------
Reporter: ncohen | Owner: mhansen
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.3.1
Component: combinatorics | Keywords:
Work_issues: | Author:
Upstream: N/A | Reviewer:
Merged: |
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Description changed by ncohen:
Old description:
> As the title says, the Birkhoff–von Neumann Theorem
> (http://en.wikipedia.org/wiki/Birkhoff%E2%80%93von_Neumann_Theorem) says
> that any doubly stochastic matrix (
> http://en.wikipedia.org/wiki/Doubly_stochastic_matrix ) can be written as
> a convex sum of permutations.
>
> This patch requires several other patches to be applied first ( or merged
> into Sage ) :
>
> * #7270 Linear Programming class
> * #7268 or #7333 as a LP solver
> * #7593 Matching function
>
> It may be better to review these patches before this very one.
>
> Nathann
New description:
As the title says, the Birkhoff–von Neumann Theorem
(http://en.wikipedia.org/wiki/Birkhoff%E2%80%93von_Neumann_Theorem) says
that any doubly stochastic matrix (
http://en.wikipedia.org/wiki/Doubly_stochastic_matrix ) can be written as
a convex sum of permutations.
This patch requires several other patches to be applied first ( or merged
into Sage ) :
* #7270 Linear Programming class
* #7268 or #7333 as a LP solver
* #7593 Matching function
Nathann
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7492#comment:4>
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