# Questions tagged [birkhoff-polytopes]

The Birkhoff polytope is a convex polytope whose points are doubly stochastic matrices and whose vertices are permutation matrices.

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### Can Sinkhorn's algorithm reach any point on the Birkhoff polytope?

It is well known that Sinkhorn's algorithm converges to a doubly stochastic matrix given a non-negative square input matrix. Knowing that Sinkhorn's algorithm always produces a DSM, I am interested in ...
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### What are the facets of the Birkhoff Polytope when $n=2$?

I've read in several sources that the number of facets of the Birkhoff polytope $\mathcal{B}(n)$ is $n^2$. Is this supposed to hold when $n=2$? Since $\mathcal{B}(2)$ has dimension $1$, the facets ...
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### Facets of the Birkhoff polytope

I recently became interested in the geometric structure of the Birkhoff polytope since it's connected to a problem that I'm working on. The Wikipedia article states that the Birkhoff polytope has $n^2$...
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### Is there a representational face lattice for the tridiagonal Birkhoff polytope?

Is there a representational face lattice for the tridiagonal Birkhoff polytope of dimension d; i.e., $\Omega^t_{d+1}$? That is, is there a system of representing the faces of $\Omega^t_{d+1}$ so that ...
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