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Topic: Surprise at my failure to resolve an issue in an elementary paper by Rado
Replies: 44   Last Post: Nov 10, 2013 12:23 PM

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 Paul Posts: 780 Registered: 7/12/10
Re: Surprise at my failure to resolve an issue in an elementary paper

Posted: Nov 4, 2013 4:51 PM

On Monday, November 4, 2013 11:53:42 AM UTC, David Hartley wrote:
>
> <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 well-known 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 f-values 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

Date Subject Author
11/3/13 Paul
11/3/13 David Hartley
11/3/13 fom
11/3/13 fom
11/3/13 fom
11/4/13 fom
11/4/13 Paul
11/4/13 Paul
11/4/13 Peter Percival
11/4/13 David Hartley
11/4/13 Paul
11/4/13 David Hartley
11/4/13 Paul
11/4/13 David Hartley
11/4/13 Paul
11/5/13 Paul
11/5/13 David Hartley
11/5/13 Paul
11/5/13 David Hartley
11/5/13 Paul
11/6/13 Paul
11/6/13 Paul
11/7/13 Paul
11/7/13 David Hartley
11/7/13 Paul
11/7/13 David Hartley
11/7/13 Paul
11/7/13 David Hartley
11/7/13 David Hartley
11/7/13 Paul
11/7/13 David Hartley
11/8/13 Paul
11/8/13 David Hartley
11/7/13 Paul
11/7/13 fom
11/8/13 Paul
11/8/13 David Hartley
11/10/13 Paul
11/10/13 David Hartley
11/10/13 Paul
11/10/13 David Hartley
11/10/13 David Hartley
11/10/13 Paul
11/4/13 Paul
11/4/13 Peter Percival