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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeSep 13th 2018
• (edited Sep 13th 2018)

discovered this ancient entry (while searching for occurences of “permutation matrix” on the nLab). This was in very bad shape, with a ill-rendering floating toc and big query box right at the beginning, then a little bit of content, and then some speculation by a contributor who we had to persuade to leave, long ago.

I did a minimum of cleaning up, in particular removed the query box, since it had been dealt with. This is what it had said:

+– {.query}

Zoran: there are several things called “Birkhoff’s theorem” in various field of mathematics and mathematical physics, and belong even to at least 2 different classical Birkhoff’s. Even wikipedia has pages for more than one such theorem. To me the first which comes to mind is Birkhoff’s factorization theorem, now also popular in Kreimer-Connes-Marcolli work and in connection to loop groups (cf. book by Segal nad Pressley). I would like that the $n$lab does not mislead by distinguishing one of the several famous Bikhoff labels without mentioning and directing to 2-3 others.

Ian Durham: Good point. I think this probably ought to be renamed the “Birkhoff-von Neumann theorem.” Is that a good enough label or should we get more specific with it?

Toby: I have moved it. See also the new page Birkhoff’s theorem, which is basically just Zoran's comment above. =–

• CommentRowNumber2.
• CommentAuthorTodd_Trimble
• CommentTimeSep 13th 2018

This is one of those interesting results that I find myself drifting back to on occasion, part of a circle of ideas which includes Hall’s marriage theorem, the latter of which I want to think about more with an eye to constructivity/categorification.