David Wilson asks:
Do all these muffin results justify a paper?
I think so.
Are they being collected anywhere?
I've been forwarding them all to Alan Frank (who asked the question in the first place), and I keep all my outgoing correspondence, so I have a very convenient archive of all muffin-conversations. Michael Kleber wrote:
If there is something coherent to say on the subject, I'd like to suggest (putting on my editor's hat) the Entertainments part of the Mathematical Intelligencer...
I had this venue in mind from the start. But I don't know how coherent the story is at this stage. David Moulton's proof about m,m+1 is great, but clearly it's just a start, and we don't even know yet whether S(km,kp) = S(m,p) for all k,m,p, which strikes me as a pretty basic thing not to know. Also, I'm worried that some of the arguments for specific pairs m,p are a bit tedious and wouldn't interest most readers once they've gleaned the general idea. At the same time, I've frequently imagined what an Intelligencer article about muffins would be like (though my imaginings have changed form as the group's discussions have evolved). One thing I've pretty consistently leaned towards is including a discussion of the process by which this body of results has been evolving. That is, I think the role of math-fun should be openly acknowledged, and that something about the nature of the group should be said, both because the social process is interesting and because there are probably a fair number of people who should be in math-fun but aren't because they don't know about it; I suspect that the overlap between this body of people and the readers of the Intelligencer is significant. (Or did Michael already "out" us in one of his columns?) Incidentally, I've been sending all the group's muffin-stuff to Alan Frank (who asked the question in the first place), and his response to the latest installment was
Thanks for keeping me posted on the muffin research. Personally, I'm just going to get my own muffin and eat the whole thing.
NOW he tells us... :-) Jim