[math-fun] Mrs. Perkins's Quilt updates
I have updated http://demonstrations.wolfram.com/MrsPerkinssQuilts/ to 40000, with many new records. The following will need updates. http://www.squaring.net/quilts/mrs-perkins-quilts.html https://oeis.org/A089046 Least edge-length ... Mrs. Perkins's quilt problem. https://oeis.org/A089047 Greatest edge-length ... Mrs. Perkins's quilt problem. ------------- Current A089046: .... 1117, 1473, 1967, 2595, 3465, 4534, 5374, 5498, 5591, 6079, 8794, 14151, 18883, ... Correct A089046: .... 1117, 1485, 1967, 2595, 3465, 4534, 5995, 7907, 10293, 13505, 17785, 23239, 31035, 39571 -------------- Current A089047: .... 4988, 5976, 7640, 9945, 13102, 17304, 23251, 31516, ... Correct A089047: .... 4988, 6443, 8568, 11357, 14877, 19594 ,26697, 34632 --Ed Pegg Jr
Ouch. It's the intent of the OEIS to (mostly) never include terms into sequences that aren't certain.
On Jul 6, 2017, at 8:42 AM, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
Current A089046: .... 1117, 1473, 1967, 2595, 3465, 4534, 5374, 5498, 5591, 6079, 8794, 14151, 18883, ... Correct A089046: .... 1117, 1485, 1967, 2595, 3465, 4534, 5995, 7907, 10293, 13505, 17785, 23239, 31035, 39571 -------------- Current A089047: .... 4988, 5976, 7640, 9945, 13102, 17304, 23251, 31516, ... Correct A089047: .... 4988, 6443, 8568, 11357, 14877, 19594 ,26697, 34632
Yes, I was thinking the same thing. For A089046 and A089047, which terms are currently known to be correct? Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Thu, Jul 6, 2017 at 9:27 AM, Hans Havermann <gladhobo@bell.net> wrote:
Ouch. It's the intent of the OEIS to (mostly) never include terms into sequences that aren't certain.
On Jul 6, 2017, at 8:42 AM, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
Current A089046: .... 1117, 1473, 1967, 2595, 3465, 4534, 5374, 5498, 5591, 6079, 8794, 14151, 18883, ... Correct A089046: .... 1117, 1485, 1967, 2595, 3465, 4534, 5995, 7907, 10293, 13505, 17785, 23239, 31035, 39571 -------------- Current A089047: .... 4988, 5976, 7640, 9945, 13102, 17304, 23251, 31516, ... Correct A089047: .... 4988, 6443, 8568, 11357, 14877, 19594 ,26697, 34632
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A089046 and A089047 -- A quilt can be based on one of two possible graphs. Polyhedral, 3-connected. All of the SPSS and SISS solutions at squaring.net are based on polyhedral graphs with a given number of edges, http://oeis.org/A002840 . Planar 2-connected. Often, a SISS solution has a non-polyhedral. My quilt solutions 2-22 are all based on non-polyhedral graphs, with two neighboring squares of the same size. The number of 2-connected planar graphs quickly becomes unmanagable. The 2-connected solutions tend to be floppy, meaning the squares can be moved around. If the neighboring squares of same size can be moved to the corners, then a build method exists to make a 3-connected quilt, with no neighboring squares of the same size. Mining the SISS-32 solutions gave me some unknown primitive 2-connected quilts down to order 26 or so. Lower orders should be fairly safe. Deep drilling to update low orders is very rare. I can only think of 3 quilts under order 5000 that needed to be updated. If SISS-33 was made available, a large effort with it might update 10 quilts of size under 15000, and likely wouldn't touch any of the records under that value. Above 15000, the best-known values I've posted can likely be beaten as soon as new SPSS / SISS orders are made available. There are many existing primitive quilts, and recursively using build methods hadn't been exhaustively tried until now. A089046 and A089047 are almost certainly correct up to 5000, and will require clearance of higher SISS and SPSS orders in order to beat any of the records I've posted. --Ed Pegg Jr On Thu, Jul 6, 2017 at 8:36 AM, Neil Sloane <njasloane@gmail.com> wrote:
Yes, I was thinking the same thing. For A089046 and A089047, which terms are currently known to be correct?
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
On Thu, Jul 6, 2017 at 9:27 AM, Hans Havermann <gladhobo@bell.net> wrote:
Ouch. It's the intent of the OEIS to (mostly) never include terms into sequences that aren't certain.
On Jul 6, 2017, at 8:42 AM, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
Current A089046: .... 1117, 1473, 1967, 2595, 3465, 4534, 5374, 5498, 5591, 6079, 8794, 14151, 18883, ... Correct A089046: .... 1117, 1485, 1967, 2595, 3465, 4534, 5995, 7907, 10293, 13505, 17785, 23239, 31035, 39571 -------------- Current A089047: .... 4988, 5976, 7640, 9945, 13102, 17304, 23251, 31516, ... Correct A089047: .... 4988, 6443, 8568, 11357, 14877, 19594 ,26697, 34632
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participants (3)
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Ed Pegg Jr -
Hans Havermann -
Neil Sloane