#7492: Decomposition of a doubly stochastic matrix as a convex sum of
permutations
(Birkhoff–von Neumann Theorem)
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Reporter: ncohen | Owner: mhansen
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.3
Component: combinatorics | Keywords:
Work_issues: | Author:
Reviewer: | Merged:
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Changes (by ncohen):
* status: new => needs_review
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.
>
> A proof and an algorithm can be found in this book :
> http://www.thi.informatik.uni-frankfurt.de/~jukna/EC_Book/
>
> 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
* #6680 Matching function
It may be better to review these patches before this very one.
Nathann
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7492#comment:2>
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