Talk:Doubly stochastic matrix

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.

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. 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... Colin.champion (talk) 09:50, 12 October 2021 (UTC)