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== Gyires proof is wrong==
In Hungary, the proof of the van der Waerden inequality given by Gyires is generally considered false. I could not, however, find any source for this on the internet.
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The Math Review linked from the page states, "Coordinated with these inequalities are conjectured inequalities for the doubly stochastic matrices in ''H''. These conjectures include the Well-known Van der Waerden conjecture...the author verifies the conjectures for small values", which makes it seem like he never claimed a proof in the first place! The paper does not seem to be easily available though, so I'm not sure about this. [[User:Kevinatilusa|Kevinatilusa]] ([[User talk:Kevinatilusa|talk]]) 19:42, 16 October 2012 (UTC)
== Non-square doubly stochastic matrices ==
There is a natural generalization of the concept of doubly stochastic matrix to non-square matrices: see, for example, http://www.jstor.org/stable/4355884
Defined in this manner, doubly stochastic matrix looks very similar to some kind of a discretized version of a bivariate copula density.
== Proof; generalisations ==
Hello – I added a proof of Birkhoff’s theorem – it’s pretty straightforward. I also mentioned trivial generalisations and the more complicated one by Caron et al referred to by the previous shy editor. Presumably Caron’s goes beyond the trivial one... [[User:Colin.champion|Colin.champion]] ([[User talk:Colin.champion|talk]]) 09:50, 12 October 2021 (UTC)
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