#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: new
Priority: major | Milestone: sage-4.3
Component: combinatorics | Keywords:
Work_issues: | Author:
Reviewer: | Merged:
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Description changed by ncohen:
Old description:
> As the title says, there is a theorem saying 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.
A proof and an algorithm can be found in this book :
http://www.thi.informatik.uni-frankfurt.de/~jukna/EC_Book/
Nathann
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7492#comment:1>
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