Consultancy Fee of $1K-$5K (US) available to someone intimate with dim 2 partial orders and ordered DAGs

From: David Halitsky (dhalitsky_at_cumulativeinquiry.com)
Date: 07/19/04 

Date: Mon, 19 Jul 2004 18:44:03 +0000 (UTC)

Cumulative Inquiry, Inc, a start-up R&D firm
chartered in Huntsville AL (USA), will pay a
consultancy fee of $1K - $5K in order to obtain
a proof of the following conjecture.

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Let o(dag) be any ordered DAG (directed acyclic
graph) in which any two vertices share either all
or none of their immediate descendants (note:
pre-ordered trees and forests pre-ordered in the
obvious way belong to the "none" leg of this
condition.)

There is then a 1:1 mapping from the set O(DAG)
of all such o(dag)'s INTO (not ONTO) the set of
all dim 2 partial orders (including the trivial
dim 1 partial order or chain.)

See two examples below for a tree and non-tree case
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Fiduciary references for prompt payment of
consultancy fees by Cumulative Inquiry Inc
can be obtained from William F. Mann at
wfmann@alum.mit.edu.

If a proof is obtained and the author thinks
it worth submitting to any peer-reviewed journal,
then rights will belong to the author of the proof.

Further, if the fee is not exhausted by proof of
the above, then the remainder can be applied to
a precise definition of those ordered DAGs which
are not in O(DAG) but are uniquely representable
by dim 2 partial orders (this is tricky and not
immediately obvious.)

Finally, if the proof is so trivial as not to be
worth even the min of the fee, could someone please
sketch out its beginning in a posting to this group ?

If the consultancy is desired, please respond to David
Halitsky

dhalitsky@cumulativeinquiry.com

David Halitsky
2928 Stewart Campbell Pte
Thompsons Station TN 37179 USA
Cell: 256-426-6243 (USA)

Thanks for any time anyone can afford to spend thinking
on this matter.

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Example of a "tree case"

partial order 1: 0 1 2 3 4 5 6
partial order 2: 0 6 1 5 2 4 3

vertices: (0,0), (1,6), (2,1), (3,5), (4,2), (5,4), (6,3)
edges: ((xi,yi),(xj,yj)) such that xi < xj and yi < yj

Example of a "non-tree" case

partial order 1: 0 1 2 3 4 5 6
partial order 2: 0 2 1 6 5 4 3

vertices: (0,0), (1,2), (2,1), (3,6), (4,5), (5,4), (3,3)
edges: ((xi,yi),(xj,yj)) such that xi < xj and yi < yj

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