Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
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. =–
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.
1 to 2 of 2