Acknowledgment of Dr. Donald Knuth's role in formulation of the "DAG/POSET" conjecture

From: David Halitsky (dhalitsky_at_cumulativeinquiry.com)
Date: 08/05/04 

Date: 5 Aug 2004 07:43:22 -0700

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Background reference threads at sci.math for this thread are:

1)
DAG/POSET "consultancy fee" conjecture: sole thread here for all future postings

2)
counting posets,dim=2

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Posting:

The "DAG/POSET" conjecture posted to sci.math has engendered
solid work at the two threads referenced above. Interim
results at the first thread above will solidify with the
return from vacation of Dr. David Wagner, who will review
the work of Rieper/Stertenbrink/Houston/Busygin/Brown
and clarify/correct (if necessary) and expand.

Because the "DAG/POSET" conjecture can now be considered
legitimate (though "wrong,wrong.wrong" in my initial
entirely ignorant formulation), I feel it necessary
to acknowledge Dr. Donald Knuth's contribution to the
formulation of this problem.

At the URL:

http://www.CumulativeInquiry.com/StrucClues/knuth.pdf

there is a reproduction of a 2-page handwritten note from Dr. Knuth,
which he was kind enough to send in February 03 concerning my
claim that "orderable DAGs" are 1:1 with dim 2 posets, and that
this claim needs only a "proof without words" because it is
essentially trivial. (Talk about "ignorant" - how "ignorant"
was that?)

If one takes a moment to scan Dr. Knuth's note, it will be
seen that he anticipated virtually all of the problems and
relevant cases which have motivated the discussion in the two
sci.math threads noted above.

So, I felt it was proper to note his original contribution
to this effort, inasmuch as I would not have bothered professional
mathematicians about the matter were it not for the implicit
encouragement in Dr. Knuth's remark that the "DAG/POSET" conjecture
opens up "interesting and new" ground.

Please note also that Dr. Knuth, sometime ago, explicitly
gave me permission to acknowledge his comments in the above-
referenced pdf, once the "DAG/POSET" conjecture had been
deemed legitimate by the relevant community(ies). I believe
that the work already done and to be done at the above two threads
satisfies this condition imposed by Dr. Knuth.

Finally, please note that the work engendered by Dr. Knuth's
original observations (i.e. the work at the two above-referenced
threads) is precisely the reason why "Cumulative Inquiry, Inc."
was named "Cumulative Inquiry."

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