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Gil Kalai
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Generalizations of the Birkhoff-von Neumann Theorem

The famous Birkhoff-von Neumann theorem asserts that every doubly stochastic matrix can be written as a convex combination of permutation matrices.

The question is to point out different generalizations of this theorem, different "non-generalizations" namely cases where an expected generalization is false, and to briefly describe the context of these generalizations.

A related MO question: Sampling from the Birkhoff polytope

Gil Kalai
  • 24.7k
  • 38
  • 235
  • 327