Paul
Posts:
764
Registered:
7/12/10


Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
Posted:
Nov 4, 2013 4:51 PM


On Monday, November 4, 2013 11:53:42 AM UTC, David Hartley wrote: > In message <108bdb66f2204d28991e5318f87ffcb9@googlegroups.com>, Paul > > <pepstein5@gmail.com> writes > > >Thanks very much for this correction. I will use this corrected > > >version of L and attempt to understand the rest of the paper. I agree > > >that this corrected L gets past the blockage I initially complained > > >about. I look forward to reading the rest of the paper and I hope that > > >correcting L in this way doesn't cause problems further on in the proof. > > > > It was getting late last night and I didn't look any further. Having had > > a quick glance now it looks like the second part of the proof uses the > > original definition of L. I'll look more closely tonight but at the > > moment it looks like the proof can't be saved by redefining L. > > Andreas Blass (who has made wellknown contributions to combinatorics and other fields) answered at Math Overflow.
Here is his response: I think you're overlooking the fact that g , defined at the top of page 2, is constant on [B ? ] 2r (and therefore on [B] 2r ). This means that, as long as the y i ,y ? i ,z i and z ? i are drawn from B ? , equality of fvalues at any two of these r tuples depends only on the relative sizes of the 2r numbers in those two r tuples. So one can indeed go from information about some two r tuples to information about every pair of "similarly configured" r tuples. ...
This sounds like enough of a hint that I can resolve the gap. It's not totally transparent yet but it probably will be in about 10 minutes. (I just saw his post a few moments ago).
Thanks.
Paul Epstein

