[math-fun] 4-orchard problem
I recently tackled the 3-orchard problem. Nice pictures are at http://oeis.org/A003035 . The 4-orchard problem is proving harder because the solutions don't seem as strong. In particular, the solutions for 22-25 points seem easily beatable. I've posted values and a picture at https://math.stackexchange.com/questions/2554709/the-4-orchard-problem If anyone can improve these solutions, please let me know. --Ed Pegg Jr
I have always wondered if 3-orchard could be tackled topologically. For example, suppose primitive A-B-C denotes that distinct points A, B, and C occur on a line in that order. We could formulate some constraints related to betweenness, e.g. not A-B-A not A-B-B if (A-B-C and A-C-D) then A-B-D and planarity(?) and 3-orchard constraints if A-B-C then not B-C-D The object would be to devise a handful of axioms of this sort that would be sufficient to show whether or not a pile of A-B-C statements is consistent with a 3-orchard configuration without having to assign geometric locations to the points.
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Ed Pegg Jr Sent: Wednesday, December 06, 2017 7:08 PM To: math-fun Subject: [math-fun] 4-orchard problem
I recently tackled the 3-orchard problem. Nice pictures are at http://oeis.org/A003035 .
The 4-orchard problem is proving harder because the solutions don't seem as strong. In particular, the solutions for 22-25 points seem easily beatable. I've posted values and a picture at https://math.stackexchange.com/questions/2554709/the-4-orchard- problem
If anyone can improve these solutions, please let me know.
--Ed Pegg Jr _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Do we need betweenness at all? The whole setup is projective -- n points forming r rows is equivalent to n lines forming r 'stars', where a star is three lines meeting at a point (with the added restriction that no four lines meet at a point). On Fri, Dec 15, 2017 at 10:24 PM, David Wilson <davidwwilson@comcast.net> wrote:
I have always wondered if 3-orchard could be tackled topologically.
For example, suppose primitive A-B-C denotes that distinct points A, B, and C occur on a line in that order.
We could formulate some constraints related to betweenness, e.g.
not A-B-A not A-B-B if (A-B-C and A-C-D) then A-B-D
and planarity(?)
and 3-orchard constraints
if A-B-C then not B-C-D
The object would be to devise a handful of axioms of this sort that would be sufficient to show whether or not a pile of A-B-C statements is consistent with a 3-orchard configuration without having to assign geometric locations to the points.
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Ed Pegg Jr Sent: Wednesday, December 06, 2017 7:08 PM To: math-fun Subject: [math-fun] 4-orchard problem
I recently tackled the 3-orchard problem. Nice pictures are at http://oeis.org/A003035 .
The 4-orchard problem is proving harder because the solutions don't seem as strong. In particular, the solutions for 22-25 points seem easily beatable. I've posted values and a picture at https://math.stackexchange.com/questions/2554709/the-4-orchard- problem
If anyone can improve these solutions, please let me know.
--Ed Pegg Jr _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
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David Wilson -
Ed Pegg Jr -
Michael Collins